# Towards Openness Beyond Open Access: User Journeys through 3 Open AI
Collaboratives

Jennifer Ding
The Alan Turing Institute
<EMAIL_ADDRESS>
Christopher Akiki
Leipzig University
<EMAIL_ADDRESS>
Yacine Jernite
Hugging Face
<EMAIL_ADDRESS>
Anne Lee Steele
The Alan Turing Institute
<EMAIL_ADDRESS>
Temi Popo
Mozilla Foundation
<EMAIL_ADDRESS>

###### Abstract

Open Artificial Intelligence (Open source AI) collaboratives offer alternative
pathways for how AI can be developed beyond well-resourced technology
companies and who can be a part of the process. To understand how and why they
work and what additionality they bring to the landscape, we focus on three
such communities, each focused on a different kind of activity around AI:
building _models_ (BigScience workshop), _tools/ways of working_ (The Turing
Way), and _ecosystems_ (Mozilla Festival’s Building Trustworthy AI Working
Group). First, we document the community structures that facilitate these
distributed, volunteer-led teams, comparing the collaboration styles that
drive each group towards their specific goals. Through interviews with
community leaders, we map user journeys for how members discover, join,
contribute, and participate. Ultimately, this paper aims to highlight the
diversity of AI work and workers that have come forth through these
collaborations and how they offer a broader practice of openness to the AI
space.

##  1 Introduction

While the majority of AI production and resources are concentrated within
technology companies in the US, Europe, and China (Savage, 2020), the growth
of open AI collaboratives offer alternative pathways for how AI is developed
and who is able to be a part of the process. In addition to creating open-
access resources, these online, distributed, and largely volunteer-led
collaboratives create new opportunities for more people from outside of the
technology field to participate in the process of building, deploying, and
governing AI. This kind of environment enables more actors and activities to
become open for a broader practice of open AI.

This paper highlights three open AI communities each focused on a different
kind of activity around AI—building _models_ (BigScience Workshop),
_tools/ways of working_ (_The Turing Way_) (The Turing Way Community, 2022),
and _ecosystems_ (Mozilla Festival’s Trustworthy AI Working Group)—and typical
user journeys taken by their members to discover, join, contribute, and lead
within the team. Though there are other such communities, these three were
chosen due to the availability of open materials (e.g. meeting notes or
project documentation via platforms like GitHub and Hugging Face Hub) and
regular meetings open to the public. In addition to referencing public
community materials, we have conducted qualitative interviews with community
leaders to understand explicit and implicit structures that influence member
experience.

Figure 1: User journeys through open AI communities

##  2 Community Structures

### BigScience Workshop

The BigScience Workshop was a value-driven (Elliott, 2017) research initiative
modeled after large-scale collaboration schemes from the second half of the
twentieth century (Longino, 2019) to address research challenges in particle
physics, genetics, and astronomy by convening large groups of researchers
organized in specialized subgroups and instrumentalizing specialized hardware.
Inspired by these initiatives, BigScience Workshop assembled over 1000
volunteer researchers from May 2021 to July 2022, to work together toward
training the BLOOM (BigScience Large Open-science Open-access Multilingual)
Language Model. The workshop was composed of working groups focusing on topics
like multilinguality, evaluation of bias-fairness, data governance, and
environmental impact (see: Figure 2). Though the workshop has ended, members
continue to collaborate, though with less intensity than before. Through
GitHub contributor records, we find that members come from countries such as
France, US, India, Saudi Arabia, Indonesia, Germany and Singapore.

### The Turing Way

Created in 2019, _The Turing Way_ is a distributed community of researchers
and practitioners from data-science related fields who are co-creating a
handbook of tools and best practices to ensure that conducting open,
responsible, localised, and collaborative data science is "too easy not to
do.” The book is co-written by over 400 volunteers in multiple languages
through GitHub, which serves as a data store, text version control, and an
asynchronous collaboration tool (see: Figure 3). The community convenes
through i) bi-weekly Collaboration Cafes for co-working and ii) biannual Book
Dash events for community strategizing, as well as contributing to and
maintaining the repo. _The Turing Way_ handbook is composed of five guidebooks
for Reproducible Research, Project Design, Communication, Collaboration, and
Ethical Research. Through GitHub contributor records, we find that members
come from countries such as the UK, The Netherlands, India, Saudi Arabia,
Argentina, and the US (The Turing Way Community, 2022).

### Mozilla Festival’s Trustworthy AI Working Group

As part of the Mozilla community, the Building Trustworthy AI Working Group is
composed of over 400 global members who collaborate on projects selected by
the core leadership team. The TAIWG is led by a chair and members include
project leads and volunteers who join projects they are interested in (see:
Figure 3). The TAIWG began in 2020 and it runs on an annual schedule, with
cohorts of projects kicking off in the Fall to work towards the Mozilla
Festival in the Spring. Over 20 projects have graduated so far, and past
projects include MOSafely: An AI Community Making the Internet a Safer Place
for Youth, a feminist dictionary in AI and AI Governance in Africa. On the
working group page, we see that members come from countries like South Africa,
Canada, US, and the UK.

Figure 2: Division of BigScience Workshop into working groups

##  3 User Journeys

To understand the range of member experiences within the three open AI
communities, we have conducted interviews with community leaders to map user
journeys for key points in a member’s experience with a community:
discovering, joining, contributing, and leading.

### Discovering

Engaging with a community begins with discovery, a growing challenge in AI
where new initiatives are emerging rapidly. For all three communities, the
influence of prominent members and the reputation of organizations supporting
the groups (e.g. HuggingFace, The Alan Turing Institute, and Mozilla
Foundation) played important roles. However, in order to expand reach beyond
existing networks, the communities applied tactics to diversify their
membership. BigScience’s founding team took steps to outreach outside their
geographical and professional domains through situated events like local data
hackathons. _The Turing Way_ seeks out collaborations with open science
organizations around the world to build off each other’s work and connect
their communities. The MozFest TAIWG is made up of engaged members from the
Mozilla Festival Community and the Mozilla Developer Community. To expand our
reach, they have also invited participation from local partners in cities
where the Mozilla Festival is held.

A common draw for new members is in a shared challenge and space for
addressing it. Whether it’s an openly developed LLM, improving research
culture, or building trustworthy AI, the communities center on a direction of
AI work that may not be accessible elsewhere for aspiring members.

### Joining

Joining is an important point in a user journey that can be defined by the
barriers presented. A comparison can be made to the process of joining an
academic or industry AI research lab, where an individual must undergo years
of accreditation and a gauntlet of interviews to even be considered for entry.
This process is a major limiting factor, and as AI becomes more impactful in
everyday life, this barrier to entry exacerbates the power dynamic between AI
producers and everyone else.

In contrast, each of the three collaboratives is open to any interested
participant who typically find out about the community and join through
digital doorways such as an online channel (e.g. email listserv, Twitter),
collaboration space (e.g. Slack), or video call meeting or event (e.g. Zoom).
Because these channels are available to anyone with access to these online
resources, this means many more people in different time zones, backgrounds,
and skill levels can enter.

While lowering the barrier to entry is the first step to the joining process,
it is not enough to facilitate active participation. In our conversations with
community leaders, they shared that the act of “lurking” is common practice
and not something to be stigmatized Chen and Chang (2013). Whether it’s
listening in on meetings or consuming and reacting to content on Slack, this
behavior is characteristic of digital spaces and offers an easy, safe way to
explore the community before contributing.

Figure 3: Left: MozFest Trustworthy AI Working Group Cohort 3, Right: _The
Turing Way_ Roles

### Contributing

After a member has passed through the digital doorway to join a community, the
next step in their user journey is to begin contributing. Community leaders
remarked on how the kinds of available "jumping in" points varied by the stage
of the community. This was particularly important for BigScience and the TAIWG
which have hard deadlines associated with working groups, which members join
based on their skill sets and interests. Because the core activity for _The
Turing Way_ is co-writing, members can easily join at any point in time.
However, the process of contributing via GitHub may not be straightforward to
new members. Thus, first contributions often require a new member to pair with
older members who guide them through the process.

Because contributing to all three communities is voluntary, the question
arises for what motivates members to contribute. Community leaders shared that
members are often driven by an interest in working on a problem that they are
not able or empowered to do in their normal jobs, to gain skills and
experience in AI, and capture their work in papers, blog posts, tools, or
presentations. However, they also shared that identifying opportunities to
“give back” to members is important, whether through awards/recognition or
connecting them to other opportunities in the community and beyond.

### Leading

Leadership takes on different forms within all three communities. In addition
to more traditional leadership roles such as leading a working group, program
and community management were also leadership roles that the communities
invested in. The glue work associated with these latter roles is important for
many collaborations, and crucial for these collaboratives where membership is
composed of global volunteers.

Typical leadership pathways come from an invitation from an existing leader or
through responsibility for a core work stream. In BigScience and _The Turing
Way_ , there are leadership roles filled through a formal hiring process via
HuggingFace and The Alan Turing Institute, respectively. Hired members serve
as a core engine to drive the project forward during working hours, managing
funding and logistics and providing infrastructure and resources. However, any
member can, through expertise or initiative, propose a new project to lead and
recruit collaborators to carry it through.

Community leaders shared stories of moments where a member was formally or
informally empowered to leadership. These ranged from small actions such as
being asked to share their opinion in a meeting to longer processes where
continuous work on a project organically led to a member’s implicit status as
the de facto owner of it. Because all three communities draw people from a
range of backgrounds, who may not see themselves as “technical” or “AI
experts”, the communities offer a form of accreditation and empowerment
through association with the group and recognition on research papers and
through official titles (e.g. “AI Builder” in MozFest TAIWG).

##  4 Towards a broader definition open AI

BigScience Workshop, _The Turing Way_ , and MozFest’s Building Trustworthy AI
Working Group provide examples for how AI collaborations can diversify,
democratize, and broaden our understanding of what open AI means. In addition
to creating space for more people to join in and contribute to the AI field,
they have also constructed environments where new ideas can emerge and new
people are empowered to carry them out. Our community research shows that by
lowering the barriers to entry through public, digital doorways and by
creating space for new research directions, open AI collaboratives fill an
important gap in the wider AI ecosystem. These three communities offer new
frameworks to empower more people around the world to participate and shape
the AI ecosystem in ways that are meaningful to them. Though some of these
groups may disband in time, their example can serve as a template for future
collaborations and to help accelerate a broader practice of open AI.

## Acknowledgments and Disclosure of Funding

This work was supported by Towards Turing 2.0 under the EPSRC Grant
EP/W037211/1 & The Alan Turing Institute’. This work was supported by Wave 1
of The UKRI Strategic Priorities Fund under the EPSRC Grant EP/T001569/1 and
EPSRC Grant EP/W006022/1, particularly the “Tools, Practices & Systems” theme
within those grants & The Alan Turing Institute’.

The BigScience Workshop was granted access to the HPC resources of the
Institut du développement et des ressources en informatique scientifique
(IDRIS) du Centre national de la recherche scientifique (CNRS) under the
allocation 2021-A0101012475 made by Grand équipement national de calcul
intensif (GENCI). Model training ran on the Jean-Zay cluster of IDRIS, and we
thank the IDRIS team for their responsive support throughout the project, in
particular Rémi Lacroix.

This work was made possible by the Mozilla Foundation and its generous
community, particularly the MozFest Trustworthy AI working group for AI
Builders. We are thankful for the colleagues - past and present, community
members, and project leads that help us build a healthier internet and more
equitable automated future for all.

## References

  * Chen and Chang (2013) Chen, F.-C. and H.-M. Chang (2013).  Engaged lurking: The less visible form of participation in online small group learning.  Research and Practice in Technology Enhanced Learning 8(1), 171–199.
  * Elliott (2017) Elliott, K. C. (2017, 02).  A Tapestry of Values: An Introduction to Values in Science.  Oxford University Press.
  * Longino (2019) Longino, H. (2019).  The Social Dimensions of Scientific Knowledge.  In E. N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy (Summer 2019 ed.). Metaphysics Research Lab, Stanford University.
  * Savage (2020) Savage, N. (2020).  The race to the top among the world’s leaders in artificial intelligence.  Nature 588(7837), S102–S102.
  * The Turing Way Community (2022) The Turing Way Community (2022, July).  The Turing Way: A handbook for reproducible, ethical and collaborative research.


# Tunable quantum criticality in multi-component Rydberg arrays

Natalia Chepiga  Kavli Institute of Nanoscience, Delft University of
Technology, Lorentzweg 1, 2628 CJ Delft, The Netherlands

(August 28, 2024)

###### Abstract

Arrays of Rydberg atoms have appeared as a remarkably rich playground to study
quantum phase transitions in one dimension. One of the biggest puzzles that
was brought forward in this context are chiral phase transitions out of
density waves. Theoretically predicted chiral transition out of period-four
phase is still pending experimental verification mainly due to extremely short
interval over which this transition is realized in a single-component Rydberg
array. In this letter we show that multi-component Rydberg arrays with extra
experimentally tunable parameters provide a mechanism to manipulate quantum
critical properties without breaking translation symmetry explicitly. We
consider an effective blockade model of two component Rydberg atoms. Weak and
strong components obey nearest- and next-nearest-neighbor blockades
correspondingly. When laser detuning is applied to either of the two
components the system is in the period-3 and period-2 phases. But laser
detuning applied to both components simultaneously stabilizes the period-4
phase partly bounded by the chiral transition. We show that relative ratio of
the Rabi frequencies of the two components tunes the properties of the
conformal Ashkin-Teller point and allows to manipulate an extent of the chiral
transition. The prospects of multi-component Rydberg arrays in the context of
critical fusion is briefly discussed.

###### pacs:

75.10.Jm,75.10.Pq,75.40.Mg

Introduction. Understanding the nature of quantum phase transitions in low-
dimensional systems is a central topic of condensed matter physicsGiamarchi
(2004); Tsvelik (2003). One of the most debated and long-standing problem in
the theory of phase transitions is a chiral melting of the density-wave order
that roots back to the study of adsorbed monolayersden Nijs (1988); Schreiner
_et al._ (1994); Abernathy  _et al._ (1994); Selke and Yeomans (1982); Huse
and Fisher (1982); Huse  _et al._ (1983); Huse and Fisher (1984). Recent
experiments on Rydberg atoms attracts new attention to this problem now in the
context of one-dimensional (1D) quantum chainsKeesling  _et al._ (2019);
Chepiga and Mila (2019a, b); Maceira  _et al._ (2022); Giudici  _et al._
(2019); Chepiga and Mila (2021); Whitsitt  _et al._ (2018); Samajdar  _et al._
(2018); Rader and Läuchli (2019). The microscopic Hamiltonian of a Rydberg
array can be formulated in terms of hard-core bosons:

$\displaystyle
H_{\text{Ryd}}=\sum_{i}\left[-\Omega(d^{\dagger}_{i}+d_{i})-\Delta
n_{i}+\sum_{R=1}^{+\infty}V_{R}n_{i}n_{i+R}\right]$ (1)

where $\Omega$ is a Rabi frequency and $V_{R}\propto R^{-6}$ is the van der
Waals potential. The competition between the laser detuning $\Delta$ that
keeps atom in a Rydberg state and strong van der Waals interaction that blocks
simultaneous excitation of multiple atoms within a certain radius realizes a
sequence of density-wave lobes with integer periodicities $p=2,3,4,...$
Keesling  _et al._ (2019); Rader and Läuchli (2019). These ordered phases are
surrounded by the disordered phase with incommensurate short-range order.
Incommensurability signals chiral perturbations in a system that have a
drastic effect on the nature of quantum phase transitionsHuse and Fisher
(1982); Ostlund (1981); Huse and Fisher (1984).

For $p=2$ chiral perturbations do not appear and the transition, if
continuous, is in the Ising universality class. For $p\geq 5$ the transition
takes place via an incommensurate Luttinger liquid phase (also known as a
floating phase)Rader and Läuchli (2019). The transition out of $p=3$ phase is
more complicated. Inside the disordered phase chiral perturbations vanish
along commensurate lines with wave-vectors $q=2\pi/p$. At the point where a
commensurate line hits the boundary of the period-3 phase the transition is
conformal in the three-state Potts universality class. Away from this point
chiral perturbations are relevant and the transition is believed to be in the
Huse-Fisher chiral universality classHuse and Fisher (1984); Samajdar  _et
al._ (2018); Chepiga and Mila (2019b); Giudici  _et al._ (2019); Maceira  _et
al._ (2022). When chiral perturbations are strong a chiral transition is
eventually replaced by a floating phaseChepiga and Mila (2019b); Rader and
Läuchli (2019); Maceira  _et al._ (2022).

The most intriguing case is $p=4$. Along the commensurate line $q=\pi/2$ the
transition is conformalChepiga and Mila (2021) however the underlying Ashkin-
Teller critical theory forms a weak universality classKohmoto  _et al._
(1981); Di Francesco  _et al._ (1997). This implies that critical exponents,
for instance $\nu$ that describes a divergence of the correlation length, can
be continuously tuned by an external parameter $\lambda$Kohmoto  _et al._
(1981). The Ashkin-Teller model interpolates between two decoupled Ising
chains at $\lambda=0$ and the symmetric four-state Potts point at $\lambda=1$
(see Fig.1). The exponent $\nu$ as a function of $\lambda$ is known
exactlyKohmoto  _et al._ (1981); O’Brien  _et al._ (2015):

$\nu=\frac{1}{2-\frac{\pi}{2}[\arccos(-\lambda)]^{-1}}.$

As sketched in Fig.1 the effect of chiral perturbations that appear in Rydberg
arrays away from the commensurate line change the nature of the transitionHuse
and Fisher (1984); den Nijs (1988); Nyckees and Mila (2022); Lüscher  _et al._
(2023). When $\nu\gtrsim 0.8$ chiral perturbations immediately open a floating
phase; when $0.8\gtrsim\nu\geq(1+\sqrt{3})/4$ chiral perturbations are also
relevant but for a while the transition is direct in the chiral universality
classNyckees and Mila (2022); Lüscher  _et al._ (2023); finally, when
$(1+\sqrt{3})/4>\nu\geq 2/3$ chiral perturbations are irrelevant and for a
certain interval the transition is in the Ashkin-Teller universality class
that upon increasing chiral perturbations is followed first by the chiral
transition and then by the floating phaseSchulz (1983); Lüscher  _et al._
(2023). In the single-component Rydberg array the conformal Ashkin-Teller
point has critical exponent $\nu\approx 0.78$ and the second scenario is
realizedChepiga and Mila (2021). However, as illustrated in Fig.1, the closer
is the Ashkin-Teller point to $\nu\approx 0.8$ the shorter is the interval of
the chiral transition. As a consequence, the chiral transition in a Rydberg
array appears only very close to the conformal pointMaceira  _et al._ (2022)
making its experimental investigation extremely difficult.

Figure 1:  Nature of the quantum phase transition between the period-four and
disordered phases. Vertical axis states for some relevant operator that brings
a system from the disoreder to the period-4 phase. Orange line states for the
conformal Ashkin-Teller transition. Yellow and orange regions at finite chiral
perturbations correspond to direct chiral and Ashkin-Teller transitions. Blue
and red surfaces indicate Pokrovsky-Talapov and Kosterlitz-Thouless
transitions with a floating phase between the two. Green line states for the
Lifshitz line.

In this letter we directly address this problem and show how to manipulate
quantum critical properties and to enlarge an extent of the chiral transition
with two-component bosonic Rydberg array (see below). We show that the ratio
between Rabi frequencies of the two components tunes the properties of the
Ashkin-Teller multicritical point that in turn controls an appearance and an
extent of the chiral transition.

Multi-component Rydberg atoms. Rydberg arrays defined in Eq.1 have two
independent parameters while the phase diagram of the chiral Ashkin-Teller
modelLüscher  _et al._ (2023) sketched in Fig.1 requires at least three. In
recent years there were several proposals aiming to extend the set of control
parameters in Rydberg atomsSingh  _et al._ (2022); Sheng  _et al._ (2022);
Levi  _et al._ (2015); Lan  _et al._ (2016); Eck and Fendley (2023); Beradze
_et al._ (2023); Fromholz  _et al._ (2022). Among them the multi-speciesSingh
_et al._ (2022); Sheng  _et al._ (2022) and the multi-componentLevi  _et al._
(2015); Lan  _et al._ (2016) Rydberg arrays seems the most promising. In
multi-species setup a certain arrangements of Cs and Rb atoms is prepared.
Rabi frequency, laser detuning and van der Waals potential can be individually
controlled for each individual specimen in addition to the inter-species
interaction, so the effective model spans over six-dimensional parameter
space. In multi-component Rydberg atoms, only one type of atoms is used but
each atom can be excited to one of the two Rydberg levels - components as
sketched in Fig.2. The levels can be selected such that (i) first-component
interaction is much stronger than the second component one; and (ii) all other
interactions including those between different components are negligibly
small. This model has five independent parameters: inter-atomic spacing, two
Rabi frequencies $\Omega_{1}$ and $\Omega_{2}$ and two individually controlled
laser detunings $\Delta_{1}$ and $\Delta_{2}$ (see Fig.2). Between two set-ups
- multi-species and multi-component arrays - the latter has one significant
advantage in the context of quantum phase transition and chiral melting: it
preserves translation symmetry.

Figure 2: Sketch of the two-component Rydberg atom. (a) Atoms are excited to
the two Rydberg levels $\alpha=1,2$ from the ground state by a laser with Rabi
frequency $\Omega_{\alpha}$ and detuning $\Delta_{\alpha}$. (b) Interaction
within the strong (magenta) and weak (blue) components result in a nearest-
and next-nearest-neighbor blockades. Configurations that violate these
blockades are marked with red ellipses.

The blockade model. Because of the very fast increase of the van der Waals
potential at short distances simultaneous occupation of atoms within certain
blockade radius is essentially excluded. It allows us to approximate long-
range interactions of two components with two types of Rydberg blockade:
nearest-neighbor blockade for the weak and next-nearest-neighbor one for the
strong components. This effectively fixes two parameters - relative
interaction strength of two species and an interatomic distance. The resulting
model is defined by the following microscopic Hamiltonian acting in a
constrained Hilbert space:

$H_{\text{MC}}=\sum_{\alpha=1,2}\sum_{i}\left[-\Omega_{\alpha}(d^{\dagger}_{\alpha,i}+d_{\alpha,i})-\Delta_{\alpha}n_{\alpha,i}\right]$
(2a) $n_{1,i}n_{1,i+1}=n_{2,i}n_{2,i+1}=n_{2,i}n_{2,i+2}=n_{1,i}n_{2,i}=0.$
(2b)

Here $d^{\dagger}_{\alpha,i}$ brings an atom at site $i$ from the ground-state
to a first or second Rydberg level if $\alpha=1$ or $2$ correspondingly. This
model has three independent parameters that we define as
$\Delta_{1}/\Omega_{1}$, $\Delta_{2}/\Omega_{2}$, and $\Omega_{1}/\Omega_{2}$.
We study the model with state-of-the-art DMRG algorithmWhite (1992);
Schollwöck (2005); Östlund and Rommer (1995); Schollwöck (2011) with up to
$N=907$ sites keeping up to 2500 states and performing up to 8 sweeps (see
Supplemental materialsSM  for details).

Figure 3: Phase diagrams of the blockade models defined by Eqs.2a and 2b as a
function of laser detuning of two species and for three relative ratio of Rabi
frequencies $\Omega_{1}/\Omega_{2}$. Each phase diagram contains four gapped
phases: disordered phase, and three density wave-phases with periodicity
$p=2,3$ and $4$. Typical patterns of these phases are sketched in (a) where
white circles denote atoms in the ground state, blue and red circles state for
atoms excited to the first (weak) and second (strong) Rydberg levels
correspondingly. The period-2 phase is separated from the disordered and
period-4 phases by two Ising transitions (blue squares and diamonds). The
multi-critical point (open orange circle) belongs to the Ashkin-Teller
universality class. For some interval in (a) and (b) the transition to the
period-4 phase is direct and chiral (red line). The key observation is that
the extent of the chiral transition in (b) for $\Omega_{1}/\Omega_{2}=2$ is
significantly larger than in (a) for $\Omega_{1}/\Omega_{2}=1$, while for
$\Omega_{1}/\Omega_{2}=0.5$ in (c) the floating phase (gray) opens
immediately. The transition between period-three phase and the disordered
phase is chiral (purple line) for small values of $\Delta_{1}/\Omega_{1}$ and
through a floating phase (gray) for large detuning of the weak component (see
”Methods ” for details).

Phase diagram. Our main results are summarized in three phase diagrams in
Fig.3. When laser detunings are small
$\Delta_{1}/\Omega_{1},\Delta_{2}/\Omega_{2}\ll 1$ the system is in the
disordered phase and translation symmetry is not broken. For
$\Delta_{2}/\Omega_{2}\gg\Delta_{1}/\Omega_{1}$ the system is populated with
the strong component that due to next-nearest-neighbor Rydberg blockade leads
to a period-three phase separated from the disorder phase by either chiral
transition or the floating phaseSM . In the opposite limit
$\Delta_{2}/\Omega_{2}\ll\Delta_{1}/\Omega_{1}$ the system is in the period-
two phase with every other site occupied by a weak component; the transition
to the disordered phase is in the Ising universality phaseSM . Upon increasing
the detuning $\Delta_{2}$ the system undergoes the second Ising transitionSM
where the translation symmetry is spontaneously broken once again and every
other empty site of the period-2 phase is occupied by the strong component
resulting in the period-four phase (sketched in Fig.3(a)) with broken
$\mathbb{Z}_{2}\times\mathbb{Z}_{2}$ symmetry (see Supplemental materialsSM
for further details). Upon increasing $\Delta_{2}/\Omega_{2}$ two Ising lines
come closer and eventually merge into a multicritical point in the Ashkin-
Teller universality clasDi Francesco  _et al._ (1997). Beyond this point the
transition from the disordered to the period-four phases is either direct in
the chiral universality class or via the floating phase as shown in Fig.3.
This is further suported by incommensurate correlations that weak component
develops beyond the disorder lineSM .

We distinguish three types of transitions - Ashkin-Teller, chiral and floating
phase - by looking at the product $|q-\pi/2|\times\xi$, where $q$ is
incommensurate wave-vector approaching its commensurate value with the
critical exponent $\bar{\beta}$ and $\xi$ is a correlation length diverging
with the critical exponent $\nu$. To the best of our knowledge for the Ashkin-
Teller criticality the exact value of $\bar{\beta}$ is not known but according
to Huse and Fisher $\bar{\beta}>\nu$Huse and Fisher (1982, 1984). Then for the
Ashkin-Teller point the product $|q-\pi/2|\times\xi$ is expected to vanish. By
contrast, at the chiral transition the equality $\nu=\bar{\beta}$ should hold
and $|q-\pi/2|\times\xi$ takes some finite value. In case of the floating
phase, it is separated from the disordered phase by the Kosterlitz-Thouless
transitionKosterlitz and Thouless (1973) characterized by the stretch-
exponential divergence of correlation length, at the same time the wave-vector
$q$ remains incommensurate across the transition, therefore
$|q-\pi/2|\times\xi$ diverges.

In Fig.4 we show the inverse of the correlation length and the product
$|q-\pi/2|\times\xi$ across different cuts through the transition. For
$\Omega_{1}/\Omega_{2}=1$ and $\Delta_{2}/\Omega_{2}=2.27$ presented in
Fig.4(a),(b) the divergence of the correlation length is symmetric and
numerically extracted critical exponent $\nu=\nu^{\prime}\approx 0.76\pm 0.02$
is consistent with the Ashkin-Teller critical theory; the product
$|q-\pi/2|\times\xi$ vanishes. This Ashkin-Teller point belongs to the
interval where chiral perturbations results into a chiral transitionNyckees
and Mila (2022); Lüscher  _et al._ (2023). Indeed, already at
$\Delta_{2}/\Omega_{2}=2.3$ the product $|q-\pi/2|\times\xi$ shown in Fig.4(c)
takes some finite value at the transition. This picture remains valid up to
$\Delta_{2}/\Omega_{2}=2.5$. The location of the transition is extracted by
fitting the correlation length in the period-four phaseSM . For
$\Delta_{2}/\Omega_{2}=2.6$ presented in Fig.4(d) we see a sign of divergence
of $|q-\pi/2|\times\xi$ signaling the opening of the floating phase.

Figure 4:  Inverse correlation length $1/\xi$ and product $|q-\pi/2|\times\xi$
along various cuts across the transition (a)-(d) for
$\Omega_{1}/\Omega_{2}=1$; (e)-(h) for $\Omega_{1}/\Omega_{2}=2$; and (i)-(j)
for $\Omega_{1}/\Omega_{2}=0.5$. (a),(b),(e),(f),(i) and pale symbols in (j):
vertical cut through the Ashkin-Teller point. (c),(g): vertical cuts through
chiral transitions. (d),(h) and bright symbols in (j): a cut through a
floating phase. In (a) and (e) correlation lengths are fitted with the power
law with equal critical exponents $\nu=\nu^{\prime}$ specified in each panel.
$|q-\pi/2|\times\xi$ is defined with error bars $2\times\xi^{2}/N^{2}$; we
only show errorbars if they exceed the size of the symbols. Dashed lines show
the boundary of the ordered phase extracted by fitting the correlation length,
color code corresponds to the legend in the lower part of the figure.

For the larger ratio of Rabi frequencies $\Omega_{1}/\Omega_{2}=2$ the
location of the Ashkin-Teller point is almost the same but the extracted
critical exponent is noticeably smaller $\nu\approx 0.68\pm 0.04$ (see
Fig.4(e),(f)). Beyond this point we detect the chiral transition that extends
at least up to $\Delta_{2}/\Omega_{2}=2.7$ as shown in Fig.4(g). In Fig.4(h)
for $\Delta_{2}/\Omega_{2}=2.8$ one can clearly see a divergence of
$|q-\pi/2|\times\xi$ upon approaching the floating phase. The larger interval
of the chiral transition compare to the previous case with
$\Omega_{1}/\Omega_{2}=1$ is fully consistent with smaller critical exponent
$\nu$ at the Ashkin-Teller point(see Fig.4(e)). In other words, by increasing
$\Omega_{1}/\Omega_{2}$ one can tune the multicritical Ashkin-Teller point
towards larger $\lambda$ and smaller $\nu$, that in turns lead to a longer
chiral transition as sketched in Fig.1. Note also that the difference between
the chiral transition and floating phase is more pronounced for
$\Omega_{1}/\Omega_{2}=2$.

For $\Omega_{1}/\Omega_{2}=0.5$ the multicritical point is very close to the
period-three phase and the floating phase surrounding it, as a consequence the
correlation length is very large all over the narrow window of the disordered
phase. This prevents us from fitting the divergence of the correlation length
inside the disordered phase but the product $|q-\pi/2|\times\xi$ computed
locally remains a valid measure: it goes to zero at the Ashkin-Teller point at
$\Delta_{2}/\Omega_{2}=2.4$ (see Fig.4(i)-(j)), while for
$\Delta_{2}/\Omega_{2}=2.5$ it already shows a signature of divergence
suggesting the presence of the floating phase. The latter is further supported
by the divergence of the correlation length with the Pokrovsky-Talapov
critical exponent $1/2$ (see Supplemental materials SM ). The picture is
completed by the observation that along the cut $\Delta_{2}/\Omega_{2}=2.4$
through the Ashkin-Teller point the correlation length diverges with the
critical exponent $\nu^{\prime}\approx 0.81$ that lies outside of the interval
$2/3\leq\nu\lesssim 0.8$ where chiral transition is possible. Of course,
neither this interval nor the critical exponents $\nu^{\prime}$ are exact and
we cannot exclude a possibility of a short chiral transition between
$\Delta_{2}/\Omega_{2}=2.4$ and $2.5$. But what we observe here is a very
important tendency of the Ashkin-Teller critical exponent to increase with
decreasing $\Omega_{1}/\Omega_{2}$ such that the chiral transition shrinks to
the point when it eventually disappears.

Discussion. To summarize, our results offer a novel approach to manipulate
quantum criticality in Rydberg atoms that, in particular, overcomes the
bottleneck associated with the short extent of the chiral transition. In
addition, we formulate a protocol to probe the complete phase diagram of the
chiral Ashkin-Teller model. Altogether, these provides an opportunity to
explore universal and non-universal properties of chiral transitions - a
necessary step towards a formal definition of the $p=4$ chiral universality
class. We expect our results obtained for the blockade approximation to be
qualitatively correct for the model with $1/r^{6}$ potential as soon as the
selected Rydberg levels and the lattice spacing are such that detuning of weak
and strong components alone leads to stable period-two and period-three phases
correspondingly. Multi-component Rydberg arrays opens a unique opportunity to
explore fusion rules of quantum criticalities directly on a lattice. Here we
focused on the simplest case: fusion of two Ising transitions into the Ashkin-
Teller point followed by the chiral transition. Playing with different
interaction regimes and longer blockades one can realize, for instance, a
fusion of chiral transitions. Further generalization to three and more
components is conceptually straightforward and introduces a new class of
models with multi-component Hilbert space. Multiple individually controllable
parameters enables a fine-tuning, for instance, to points with higher
symmetries.

##  I Acknowledgments

I thank Bernhard Lüscher, Samuel Nyckees and Frederic Mila for insightful
discussions on the chiral Ashkin-Teller model and to Jiri Minar for inspiring
discussion on multi-component Rydberg arrays. This work has been supported by
the Delft Technology Fellowship and it was performed in part at Aspen Center
for Physics, which is supported by National Science Foundation grant
PHY-2210452. Numerical simulations have been performed at the DelftBlue HPC
and at the Dutch national e-infrastructure with the support of the SURF
Cooperative.

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Supplemental matherial to ”Tunable quantum criticality in multi-component
Rydberg arrays”

##  II Details about the algorithm

We perform numerical simulations with DMRG algorithm in the form of
variational optimization of the matrix product states (MPS)White (1992);
Schollwöck (2005); Östlund and Rommer (1995); Schollwöck (2011). We implement
the blockade by applying a strong penalty terms
$U(n_{1,i}n_{1,i+1}+n_{2,i}n_{2,i+1}+n_{2,i}n_{2,i+2})$. We choose the penalty
to be $U=400$: this value is sufficiently strong to keep expectation value of
any of the three terms listed above below $10^{-6}$ even in the vicinity of
the transition, while this value is not too large to cause instabilities and
convergence issues. We also benchmarked our algorithm with constrained DMRG
with explicitly implemented blockadesChepiga and Mila (2021, 2019a): the two
sets of results do not have any noticeable differences. Quite surprisingly the
unconstrained DMRG with the penalty terms turns out to be more efficient for
numerical simulations of multi-component Rydberg arrays than the constrained
version of the algorithm that by construction obeys a block-diagonal
structure. In order to implement constrained DMRG for multi-component system,
we generalize the implementation of next-nearest-neighbor blockade described
in details Ref.Chepiga and Mila (2021). We span local degrees of freedom over
three consecutive Rydberg atoms as sketched in Fig.5(a). This increase the
local Hilbert space to $d=17$ listed in Fig.5(b), note that out of $3^{3}=27$
total states 10 states violating the blockades were excluded. In this
construction, every pair of consequtive MPS have share two Rydberg atoms,
therefore one can use the state of these atoms as quantum labels that create
one-to-one correspondence between auxiliary legs of MPS. Thes seven labels are
listed in Fig.5(c).

Figure 5:  Implementation of DMRG with two-site blockade. (a) We associate MPS
tensor with three consequtive Rydberg atoms. The Hilbert space of this three-
site object has dimension $d=17$ sketched in (b). Every pair of MPS share two
Rydberg atoms, the states of these two atoms sketched in (c) are used to label
auxiliary legs of MPS.

Contracting the networks block-by-block allows to reduce the memory cost
significantly, however an auxiliary bond of tensors having seven different
labels leads to a large number of rather small blocks such that an over-head
for a block-by-block operation turns out to be higher than the gain from the
lower memory cost. In DMRG simulations we reach the convergence of the systems
with up to $N=907$ sites keeping up to 2500 states and performing up to 8
sweeps; we generically discard singular values below $10^{-8}$.

##  III Additional details on various phases and boundary conditions

In this section we provide further details on various phases and on the used
boundary conditions. As explained in the main text, there are four gapped
phases: disordered, and period-2, 3 and 4. Fig.6 present local density
profiles along a chain with $N=91$ sites at various characteristic points of
the phase diagram for $\Omega_{1}/\Omega_{2}=1$. Fig.6(a) shows the density
profile at $\Delta_{1}/\Omega_{1}=1$ and $\Delta_{2}/\Omega_{2}=1$ in the
disordered phase. One can clearly see that in the bulk the density of each
component is uniform. Note that the microscopic model does not preserve the
number of particles in the weak/strong component, so the density of each
component changes continuously all over the disordered phase.

Figure 6:  Local density of the strong(red) and weak (blue) component in
various phases. Density of (a) the disordered phase at
$\Delta_{1}/\Omega_{1}=1$ and $\Delta_{2}/\Omega_{2}=1$; (b) the period-2
phase at $\Delta_{1}/\Omega_{1}=2$ and $\Delta_{2}/\Omega_{2}=0$; (c) the
period-3 phase at $\Delta_{1}/\Omega_{1}=0$ and $\Delta_{2}/\Omega_{2}=3$; (d)
the period-4 phase at $\Delta_{1}/\Omega_{1}=3$ and $\Delta_{2}/\Omega_{2}=3$;
(e) the floating phase in the vicinity of the period-4 phase at
$\Delta_{1}/\Omega_{1}=2$ and $\Delta_{2}/\Omega_{2}=3$

Fig.6(b) presents the density profile at $\Delta_{1}/\Omega_{1}=2$ and
$\Delta_{2}/\Omega_{2}=0$ in the period-2 phase where every other site is
occupied by a weak (blue) component. In the thermodynamic limit this phase is
two-fold degenerate - weak component can occupy either even or odd sites. In
addition one can still detect a small density of the strong (red) component
uniformly distributed among sites that are not occupied by a weak component.

Fig.6(c) shows the period-3 phase at $\Delta_{1}/\Omega_{1}=0$ and
$\Delta_{2}/\Omega_{2}=3$. Every third site is occupied by the strong (red)
component, while the remaining sites host a certain density of the weak
component uniformly distributed over unoccupied sites. This phase breaks
$\mathbb{Z}_{3}$ symmetry and in the thermodynamic limit it has three-fold
degenerate ground-state.

The density of the period-4 phase taken at $\Delta_{1}/\Omega_{1}=3$ and
$\Delta_{2}/\Omega_{2}=3$ is shown in Fig.6(d). One can see that every second
site is occupied by the weak (blue) component, while every other of the
remaining sites are occupied by the strong (red) component. This phase
spontaneously breaks $\mathbb{Z}_{2}\times\mathbb{Z}_{2}$ symmetry and has a
four-fold degenerate ground-state in the thermodynamic limit.

Finally, in Fig.6(e) we also present a typical density profile of the floating
phase taken in the vicinity of the period-4 phase at $\Delta_{1}/\Omega_{1}=2$
and $\Delta_{2}/\Omega_{2}=3$. Note that in the thermodynamic limit the
density in this critical phase is uniform and the presence of
incommensurability can only be detected via correlation functions.
Oscillations in local density that we observe in Fig.6(e) are visible because
of explicitly broken translation symmetry due to open boundary conditions.

As one can see in Fig.6(b)-(d), ordered phases favor occupied sites at the
edges. This impose boundary conditions to be respected in numerical
simulations: for the period-2 phase the total number of sites should satisfy
$N=2k+1$ with integer $k$. Period-3 phase requires $N=3k+1$. In the period-4
phase the edges favor weak-strong-weak cluster over the first and last three
sites implying that the chain length should satisfy $N=4k+3$. As one can
easily check $N=91,199,451,607,907$ used in this paper satisfy all three
conditions.

##  IV Location of the Ising transitions

In order to locate Ising transitions we look at the finite-size scaling of the
density oscillations - a local measure of spontaneously broken translation
symmetry. In the period-two phase the translation symmetry is broken by the
weak component and by two sites, so the relevant operator is defined as
$D_{1}=|\langle n_{1,j}\rangle-\langle n_{1,j+1}\rangle|$ that we compute in
the middle of the chain. We look at this quantity in the log-scale and
associate the transition with the separatrix that separates disordered phase
(concave curves) and the symmetry broken phase (convex ones) as shown in
Fig.7(a). The slope of the separatrix corresponds to the scaling dimension
that is in excellent agreement with the conformal field theory prediction for
the Ising transition $d=1/8$Di Francesco  _et al._ (1997).

Figure 7:  Finite-size scaling of the local density oscillations across two
Ising transitions. Scaling of the local density oscillations in (a) weak
component across the transition between the disordered and period-two phases
and (b) in strong component across the transition between the period-two and
period-four phases. In each case the separatrix is associated with the
transition and the slope agree with the Ising scaling dimension $d=1/8$
(dashed red line) shown for a reference.

At the transition to the period-four phase the translation is again
spontaneously broken: every other site that was not occupied by the weak
component in the period-two phase becomes occupied by the strong component in
the period-four phase. So the local order parameter can be defined as
$D_{2}=|\langle n_{2,j}\rangle-\langle n_{2,j+2}\rangle|$, where $j,j+2$ are
sites that are not occupied by the weak component. As previously, we associate
the transition with the separatrix and its slope is in excellent agreement
with the Ising scaling dimension $1/8$ (see Fig.7(b)).

We cross-check the nature of these two transitions by extracting the central
charge. The entanglement entropy $S_{N}(n)=-\mathrm{Tr}\rho_{n}\ln\rho_{n}$ is
extracted from the eigenvalues of the reduced density matrix $\rho_{n}$. We
extract central charge numerically from the finite-size scaling of the
entanglement entropy in an open chain that on a finite chain with $N$ sites
scales with the size of the subsystem $n$ ($1\ll n\ll N$) asCalabrese and
Cardy (2009):

${S}_{N}(n)=\frac{c}{6}\ln d(n)+s_{\mathrm{B}},$ (3)

where $d=\frac{2N}{\pi}\sin\left(\frac{\pi n}{N}\right)$ is the conformal
distance and $s_{\mathrm{B}}$ is a non-universal term that includes, in
particular, the boundary entanglement entropy. The scaling of the entanglement
entropy for the two critical points identified in Fig.7(a),(b) are presented
in Fig.7(a) and (b) correspondingly. In both cases the numerically extracted
values are in a good agreement with the theory predictions $c=1/2$. Small
discrepancy is due to a finite resolution of the location of the critical
point.

Figure 8:  Scaling of entanglement entropy at the two Ising transitions. In
each case in each case the central charge extracted with Calabrese-Cardy
formula in Eq.3 agrees with theory prediction $c=1/2$ for the Ising
transition.

##  V Extraction of the correlation length and of the wave-vector

In order to extract the correlation length and the wave-vector $q$, we fit the
connected correlation function for the strong component $C_{i,j}=\langle
n_{2,i}n_{2,j}\rangle-\langle n_{2,i}\rangle\langle n_{2,j}\rangle$ to the
Ornstein-Zernicke formOrnstein and Zernike (1914):

$C^{\mathrm{OZ}}_{{i,j}}\propto\frac{e^{-|i-j|/\xi}}{\sqrt{|i-j|}}\cos(q|i-j|+\varphi_{0}),$
(4)

where the correlation length $\xi$, the wave vector $q$, and the initial phase
$\varphi_{0}$ are fitting parameters. We extract the correlation length and
the wave-vector in two steps. First, we discard the oscillations and fit the
main slope of the decay as shown in Fig.9(a) such that the fit can be
performed in a semi-log scale $\log C(x=|i-j|)\approx c-x/\xi-\log(x)/2$. This
provides more accurate estimates of the correlation length on a long scale. In
fact, there are two very similar strategies to perform this fit: either to fit
all the points assuming that oscillations are fast enough to cancel; or to fit
only top of the arcs assuming that there are enough arcs for a reliable fit.
Here we use the second method and include the point into a fit if it exceeds
two points on its left and two points on its right. Let me emphasize here that
both methods are equivalent and affect only an amplitude and a centering of a
cosine function in the next step.

In the second step we fit the reduced correlation function

$\tilde{C}_{i,j}=C_{i,j}\frac{\sqrt{|i-j|}}{e^{-|i-j|/\xi+c}}$ (5)

with a cosine $\tilde{C}_{i,j}\approx a\cos(q|i-j|+\varphi_{0})$ as shown in
Fig.9(b). The agreement between the DMRG data (blue dots) and the fit (red
circles) is almost perfect. We estimate error in $q$ caused by finite-size
effects as $2\pi\xi/N^{2}$, where $2\pi/N$ is a natural step in $q$ due to
fixed boundary conditions and assuming for infinite correlation length, an
additional factor $\xi/N$ reflect the possibility to adjust $q$ at the edges
when correlation length is finite.

Figure 9:  Example of fit of the correlation function to the Ornstein-Zernicke
form. In the first step (a), we extract the correlation length discarding the
oscillations. In the second step (b), we fit the reduced correlation function
and extract the wave-vector $q$.

##  VI Transition out of period-three phase

In order to locate the boundary of the period-three phase and to identify the
nature of the transition we follow a similar procedure as for the boundary of
the period-four phase. We look at the product $|2\pi/3-q|\times\xi$ that is
expected to take a finite value if transition is chiral and diverge in the
case of intermediate floating phase. Here we expect conformal Potts point only
in the limit $\Delta_{1}/\Omega_{1}\rightarrow\infty$. We also look at the
scaling of the correlation length in the period-three phase. In Fig.10 we
provide an example of two typical cuts through the transition for
$\Omega_{1}/\Omega_{2}=1$: when it is chiral in Huse-Fisher universality class
in Fig.10(a),(b); and when it goes through an intermediate floating phase in
Fig.10(c),(d). Small increase of $|2\pi/3-q|\times\xi$ in Fig.10(b) indicates
its proximity to the Lifshitz point, where the floating phase opens.

Figure 10:  Inverse of the correlation length and the product
$|2\pi/3-q|\times\xi$ along two horizontal cuts across the transition to the
period-three phase for $\Omega_{1}/\Omega_{2}=1$. (a),(b) - a cut through a
chiral transition point at $\Delta_{1}/\Omega_{1}=0.5$; (c),(d) a cut through
the floating phase at $\Delta_{1}/\Omega_{1}=1$. In (a) and (c) the
correlation lengths in the period-three phase are fitted with the power law.
Dashed blue lines show the boundary of the ordered phase extracted in (a) and
(c).

Following the same procedure we identified the boundaries of the period-three
phase for $\Omega_{1}/\Omega_{2}=2$ and $0.5$. For $\Omega_{1}/\Omega_{2}=2$
our results at $\Delta_{1}/\Omega_{1}=0$ are consistent with chiral
transition, while already at $\Delta_{1}/\Omega_{1}=0.5$ we see a presence of
the floating phase. For $\Omega_{1}/\Omega_{2}=0.5$ chiral transition is
stable up to $\Delta_{1}/\Omega_{1}=1$ and the floating phase is detected at
$\Delta_{1}/\Omega_{1}=2$.

##  VII Disorder line

Chiral perturbations usually manifest itself in incommensurate correlations.
The line where real-space correlations switch from commensurate to
incommensurate regimes is usually called in the literature the disorder line.
In order to locate this line in the disordered phase we look at the connected
correlations of the weak component. A few examples of commensurate and
incommensurate scalings are shown in Fig.11; we associate the disorder line
with the point where incommensurability disappear. Calculations were performed
with $N=67$ sites deep inside the disordered phase and with $N=91$ in the
vicinity of the multicritical point.

Figure 11:  Location of the disorder line. Scaling of the weak component
correlations as a function of distance for $\Omega_{1}/\Omega_{2}=1$ and
$\Delta_{2}/\Omega_{2}=1$. For $\Delta_{1}/\Omega_{1}<1$ one can clearly see
the presence of incommensurability that disappears for
$\Delta_{1}/\Omega_{1}>1$.

It is not always clear whether the system is commensurate or incommensurate
(see, for instance, the data for $\Delta_{1}/\Omega_{1}=1$ in Fig.11) and for
this reason there is an uncertainty in the location of disorder line. However,
our results are consistent with the disorder line hitting the period-four
phase at multi-critical point. This agree with expectation that system is
commensurate on both sides of the Ising transition. In fact the situation is
more subtle here. There are two components and two commensurate Ising
transitions. At the transition between the disordered and the period-two phase
the weak component breaks translation symmetry and this particular component
has to be commensurate in the vicinity of the transition, however the strong
component can remain incommensurate across this Ising transition. But at the
second Ising transition from period-two to period four phases it is now the
strong component that breaks the translation symmetry and thus it has to be
commensurate in the vicinity of the transition. It implies that in principle
there must be a second disorder line where incommensurability develops in the
strong component; this line can be located in the period-two or in the
disordered phase and also expected to end at the multicritical Ashkin-Teller
point.

##  VIII Divergence of the correlation length at the transition to the period-
four phase

In the main text we distinguished three critical regimes - Ashkin-Teller,
chiral and floating phase - by looking at the product $|q-\pi/2|\times\xi$. In
addition we also extract the critical exponent $\nu^{\prime}$ that controls
the divergence of the correlation length upon approaching the boundary of the
period-four phase. At the Ashkin-Teller transition $2/3\leq\nu^{\prime}\leq 1$
and the corresponding results have been presented in Fig.4 (a),(e) and (i) in
the main text. For the Pokrovsky-Talapov transition this critical exponent is
expected to take the value $\nu^{\prime}=1/2$. For chiral transition the value
of this exponent is not known. For $\Omega_{1}/\Omega_{2}=1$ and for the two
cuts that we identified as a chiral transition based on $|q-\pi/2|\times\xi$
the extracted critical exponents $\nu^{\prime}$ noticeably exceeds the value
$\nu^{\prime}=1/2$ of the Pokrovsky-Talapov transition. The results are
presented in Fig.12(a),(b). By contrast, at $\Delta_{2}/\Omega_{2}=2.6$ that
we identified as a cut through the floating phase the DMRG results are in
excellent agreement with $\nu^{\prime}=1/2$.

Figure 12:  Inverse of the correlation length on both sides from (a,b) the
chiral transition and from (c) the floating phase for
$\Omega_{1}/\Omega_{2}=1$. In each case the divergence of the correlation
length in the period-four phase is fitted with a power law with the critical
exponent $\nu^{\prime}$.

For $\Omega_{1}/\Omega_{2}=2$ and $\Delta_{2}/\Omega_{2}=2.7$ that we
associated with chiral transition the critical exponent is about
$\nu^{\prime}\approx 0.65$ (for smaller system sizes we see
$\nu^{\prime}\approx 0.68$), while for $\Delta_{2}/\Omega_{2}=2.8$ we already
see an excellent agreement with the expected square-root divergence. This
further supports our conclusion that the Lifshitz point is located in the
interval $2.7<\Delta_{2}/\Omega_{2}<2.8$.

Figure 13:  Inverse of the correlation length on both sides from (a) the
chiral transition and (b) the floating phase for $\Omega_{1}/\Omega_{2}=2$

Finally, for $\Omega_{1}/\Omega_{2}=0.5$ already at
$\Delta_{2}/\Omega_{2}=2.5$ we see that the correlation length diverges with
the critical exponent $\nu^{\prime}=1/2$ as presented in Fig.14.

Figure 14:  Inverse of the correlation length on both sides from (a) the
chiral transition and (b) the floating phase for $\Omega_{1}/\Omega_{2}=0.5$

For all cuts we see a finite-size effect in the location of the transition.
This effect is very common in Rydberg atomsMaceira  _et al._ (2022).


# Conversational Data Exploration:
A Game-Changer for Designing Data Science Pipelines

Genoveva Vargas-Solar  CNRS, Univ Lyon, INSA Lyon, UCBL, LIRIS, UMR5205,
69622VilleurbanneFrance<EMAIL_ADDRESS>,  Tania Cerquitelli
Department of Control and Computer Engineering, Politecnico di
TorinoTurinItaly<EMAIL_ADDRESS>,  Javier A. Espinosa-Oviedo
CPE, CNRS, Univ Lyon, INSA Lyon, UCBL, LIRIS, UMR5205, 69622VilleurbanneFrance
<EMAIL_ADDRESS>,  François Cheval  CPE LyonVilleurbanneFrance
<EMAIL_ADDRESS>,  Anthelme Bucaiile  CPE LyonVilleurbanneFrance
<EMAIL_ADDRESS>and  Luca Polgar  CPE LyonVilleurbanneFrance
<EMAIL_ADDRESS>
###### Abstract.

This paper proposes a conversational approach implemented by the system Chatin
for driving an intuitive data exploration experience. Our work aims to unlock
the full potential of data analytics and artificial intelligence with a new
generation of data science solutions. Chatin is a cutting-edge tool that
democratises access to AI driven solutions, empowering non-technical users
from various disciplines to explore data and extract knowledge from it.

Datasets, data exploration, conversational approach, data science

##  1\. Introduction

Cutting-edge data science (DS) techniques have proven to be an alternative
quantitative method for answering analytical and predictive research questions
from non-data science experts. The principle is to process data collections
containing observations of phenomena using mathematical models, statistics,
and artificial intelligence algorithms. Non-expert users often find it
challenging to effectively use data science methods, requiring significant
interaction between data scientists and domain experts. Due to differences in
language and expertise, mediators are needed to facilitate communication,
which can be time-consuming and effort-intensive. To bridge this skills gap,
companies can train domain experts in data science, train data scientists in
the subject matter, or create a new Mediator role. A potential solution is to
use a conversational AI mediator to fill the skill gap.

We argue that conversational approaches are a good way of (i) mediating the
expression of data exploration requirements in natural language, (ii)
transforming them into artificial intelligence-based analytics, and (iii)
providing explanatory human understandable results. Non-DS experts can compare
results, give feedback to the system, and explore different analytics branches
until satisfied. By learning from feedback and experience, the conversational
environment can adapt its process to users’ profiles.

This paper introduces Chatin (Chatbot conversatIonal data exploratioN
environment ) that proposes a conversational interface for creating data
exploration interactive sessions for non-DS experts. The environment extends
ADESCA111ADESCA implements interactive data exploration with automatically
configured algorithms and graphical results.(Bethaz and Cerquitelli, 2021)
with conversational pipelines for creating broad and comparative data
collection quantitative studies completed with the return of experiences that
can improve the behaviour of the conversation sessions and the data
exploration experience. To showcase our vision, we use a case related to
modelling gender biases in social norms. Driving the conversational
exploration of a dataset released by the United Nations, the goal is to
understand gender inequality across different countries. We focus on the
possibility of driving an intuitive data exploration conversational task.

Accordingly, the remainder of the paper is organised as follows. Section 2
synthesises existing work addressing conversational data exploration. Section
3 introduces our conversational approach and system Chatin . Section 4
illustrates the validation of our approach and system through a use case
Section 5 concludes the paper and discusses future work.

##  2\. Related work

Chatbots (Adamopoulou and Moussiades, 2020; Nagarhalli et al., 2020) have
become popular conversational interfaces for assisting humans in various
tasks. However, there is limited research on analytical chatbots that
facilitate data science conversations using (semi) structured data. We
consider two approaches and solutions reported in the literature:
_conversational data exploration_ and _conversational interfaces_ designed to
provide ad-hoc services (e.g., searching for content).
Conversational data exploration. N. Castaldo et al. (Castaldo et al., 2019)
propose a framework for designing and generating chatbots to explore data.
This approach utilizes data sources and modelling abstractions to enable
designers to define the role of critical elements in user requests.
Articulate2 (Aurisano et al., 2016) is a conversational interface for visual
data exploration that accepts natural language inputs. It enables generating
and modifying visualisations while recording the user’s requests,
visualisations, and findings. Analyza (Dhamdhere et al., 2017) enables users
to explore data through a question-and-answer feature in a spreadsheet
product. It allows them to access a revenue/inventory database for a large
sales force. V. Setlur et al. (Setlur and Tory, 2022) examined the Gricean
Maxims to design conversational interactions for data exploration, to support
ambiguity and handle intent. Hossein Hassan and Emmanuel Sirmal Silva (Hassani
and Silva, 2023) explore the role of ChatGPT in assisting data scientists with
automating data cleaning and preprocessing, model training, and result
interpretation. They assert that ChatGPT can aid with natural language
processing tasks in data science, such as language translation, sentiment
analysis, and text classification. Code Interpreter is a ChatGPT 4
plugin222https://www.datanami.com/2023/07/11/openai-releases-chatgpt-code-
interpreter-your-personal-data-analyst/ that allows users to upload and
analyze files using natural language (e.g., converting files, performing
mathematical operations, plotting data). The Code Interpreter generates Python
code that is then executed in a sandboxed environment that lasts the
conversation’s duration. The execution result (e.g. a plot) is then
incorporated into the ChatGPT conversation with an explanation of what was
done. We believe current conversational solutions offer robust tools for
creating dialogues that enable non-data science specialists to design
quantitative analytics. Our work aims to improve conversational solutions by
suggesting proactive actions to guide non-specialists in intuitively designing
quantitative analytics and exploring data to extract insights and value from
it.

Conversational bots interface building tools.
Dialogflow333https://cloud.google.com/dialogflow/docs is a natural language
understanding platform created by Google that simplifies the process of
designing and integrating a conversational user interface into mobile or web
applications. Amazon Lex is a service provided by Amazon Web Services
(AWS)444https://docs.aws.amazon.com/lex/latest/dg/what-is.html that allows
developers to embed conversational interfaces into voice and text
applications. It uses natural language understanding (NLU) and automatic
speech recognition (ASR) to create lifelike and engaging user interactions.
With Amazon Lex, you can create chatbots, virtual assistants, and other
conversational experiences that feel natural and intuitive. ParlAI (Miller et
al., 2017) is a platform designed by the Facebook AI Research (FAIR) team to
facilitate collaboration and reuse of significant dialogue tasks among
researchers. It encourages collaboration in developing NLP systems, including
integration with bots and humans. This community-based platform allows
researchers to work together to advance the field of natural language
processing and improve conversational AI. Language Understanding
(LUIS)555https://docs.microsoft.com/en-us/azure/cognitive-services/luis/what-
is-luis is a cloud-based conversational AI service developed by Microsoft. It
is designed to extract valuable information from dialogues by interpreting
user goals (intents) and distilling useful information from sentences
(entities). LUIS uses a high-quality language model to achieve this, and it
integrates seamlessly with the Azure Bot Service, making it easy to create
sophisticated bots that can understand and respond to natural language input.
Our work will use chatbot implementation tools to design and implement a
conversational interface to guide non-DS specialists through conversations to
explore data collections and produce and explain quantitative insights.
Discussion. Using conversational assistants and interfaces for querying and
processing data is not new. Approaches like _query-by-example_ (Zloof, 1977)
in the early years of relational querying, natural language-based database
querying (Őzcan et al., 2020), and visual query languages (Bhowmick and Choi,
2022) are examples of previous solutions. Conversational interaction between
users and systems includes works that address the SQL-to-NL (Natural Language)
and NL-to-SQL problems such as (Eleftherakis et al., 2021; Weir et al., 2019;
Brandt et al., 2020; Brunner and Stockinger, 2021). However, these approaches
are primarily focused on query-oriented interactions. Other approaches, such
as (Kumar et al., 2016), explore dialogue-based approaches for supporting rich
data visualisations.

In recent years, there has been a growing trend towards using high-level
visual specifications in Machine Learning (ML) studios, such as Microsoft ML
Studio, to simplify the expression and programming of data science and
analytics pipelines. However, even with these tools, technical and
mathematical expertise is still required. To address this, new strategies are
emerging that use natural language processing (NLP) interfaces to allow users
to express their requirements more intuitively and user-friendly. For example,
English can be used as a programming language for Apache Spark
666https://www.databricks.com/blog/introducing-english-new-programming-
language-apache-spark. With the emergence of ChatGPT and GitHub Copilot, this
process is becoming even more intuitive and exploratory, allowing users to
express their high-level requirements more easily.  We aim to provide a
complete dialogue with the user, moving beyond simple query-and-answer
interactions. Our goal is to guide users through data exploration, where they
can (1) intuitively use and calibrate statistical and machine learning tools
to achieve their analytics targets; (2) and, in consequence, design DS
pipelines.

##  3\. Chatin : a conversational data exploration environment

Figure 1 shows the general architecture of Chatin , a conversational
environment designed to assist users in exploring data collections and
intuitively defining data exploration pipelines. The architecture, which was
first proposed in a position paper (Bethaz et al., 2021a), is organised into
four layers: (1) The conversational layer, where the user interacts with the
system using natural language requests and provides feedback on the system’s
output. (2) The orchestrator layer executes the data exploration pipeline. (3)
The data processing layer, which offers tools and APIs for data processing.
(4) The storage layer, which provides support for persistent data collections,
exploration operation results, and conversations.

As shown in Figure 1:1, the conversation environment provides an interface for
the user to express their requirements in natural language. These requirements
are then transformed into one or more data processing tasks or interactions
that request additional input. The conversation relies on meta-patterns as a
reference for performing quantitative exploration tasks. The actual data
exploration, data processing (such as clustering models), assessment scores,
and visualisation tools are implemented by a backend engine that serves as a
toolkit developed in previous work (Bethaz and Cerquitelli, 2021) (see Figure
1:3).

The conversational pipelines executed by the coordinator, as shown in Figure
1:2, are performed within sessions. Requests are processed by utilizing logs
from previous explorations conducted by the system, identifying similarities
and connections between various analyses to present the most relevant and
appropriate results for the user’s request. These results can be displayed in
text, table, or graph format. The user can then assess the clarity and
usefulness of the results by providing feedback, which is added to the
exploration log and used to inform future analyses.

Figure 1. Chatin general architecture

This abstraction layer shields the user from the complexities associated with
data exploration and analysis libraries and tools, resulting in a more user-
friendly experience.

Conversational meta-patterns. The sequence diagram of the meta-conversation
between Chatin and the user is shown in Figure 2. It is a two-way interaction
initiated and concluded by the user or the system. Every user request receives
a response from the system. The system can also ask the user to do actions,
for example, providing additional information or feedback.

An example of conversational interaction can start with a dialogue where the
user and the system interact to explore the dataset and produce initial
statistical information. Instead of asking the user to know formats and
remember formulae to compute statistical metrics, the system computes the
quantitative profile directly and provides a textual explanation of the
content.

Proactive strategy: Represents a data preparation interaction. Rather than
just responding to a user request, Chatin integrates a proactive approach
during the conversation to anticipate/suggest/analyse activities and queries
that could interest the user. The proactive strategy is a novel and original
feature of Chatin compared to existing conversational chatbots.

Figure 2. Conversational meta-patterns

We have identified five types of interactions in Figure 2, involving specific
questions and answers:
\- Pattern P1: Represents a data preparation dialogue. The conversation
pattern starts with a request like "_I need help exploring the following data
collection_ " or "_I want to explore a data collection?_ ". Consequently, the
system asks the user to upload the data collection and acknowledges the action
by telling the user the file format. Then, it proposes a structural or
statistical description of the data (e.g., "_do you prefer a structural and/or
a statistical description of your data?_ ").
\- Pattern P2: Represents an analytics task request dialogue. The user can
request an analytical task, such as data modelling or prediction, while
delegating the complexity of the analysis to the system. The system can then
choose and propose a possible solution, performing the task and producing
output with explanations of the task done. Often the results are associated
with plot options so that the user decides which one s/he prefers.
\- Pattern P3: Represent an action request dialogue. The user can also request
more specific actions, such as changing the time interval for analysis or
excluding a particular attribute from future analysis.
\- Pattern P4: Represents a request input dialogue initiated by the chatbot.
The system can ask for additional input parameters in terms of interactions
initiated by the system. Additionally, the system may provide output to the
user without being specifically requested. The output type is decided
according to the user’s profile and previous experience, which can help
determine what analysis and results would be most relevant and relevant to the
user without any initial input.
\- Pattern P5: Represents a an additional output provision dialogue initiated
by the chatbot. Following the previous example of pattern P1, the system
produces various statistics from a dataset, and it can follow up by proposing
plots with a narrative description of the type of plot and how it represents
the data. For the plots, the chatbot suggests plots with explanations and asks
for feedback from the user so that she/he can choose the plots that seem more
comprehensible.
\- Pattern P6: Represents a proactive interaction initiated by the chatbot.
The system can start a conversation and suggest activities and mini-tasks
based on the system skills and expertise acquired from past interactions with
users and users’ provided feedback. The user can accept or reject the
suggestion.
The conversational meta-patterns can occur in any order. The conversation can
also be paused anytime, allowing the user to save the progress and resume
later without losing any analysis results.

Data exploration assistance: converting text to action. Once Chatin receives a
request, it divides it into tasks ordered in an execution plan. The execution
plan is a directed graph representing a solution space with data exploration
functions that can be requested according to the initial handshake. It
represents a dataflow with operations represented by nodes and edges
representing the input/output data.

The execution of a node implies resolving it to a concrete implementation in a
library or provided by an external module (e.g., transforming the dataset into
some format, performing statistical profiling, or clustering values and
producing plots). Every task in the execution plan implements an interactive
cycle that receives input, proposes/asks for input parameters, presents
results, and expects feedback.

Figure 3. Transformation conversation meta-patterns towards execution plan
patterns.

Text to action strategies: building data exploration execution plans. We have
adopted two strategies to implement the text-to-action strategy of the system.
\- Simplified text-to-action strategy: The general principle of the strategy
relies on a set of rules and a controlled vocabulary extracted from Wordnet
that contains the verbs associated with data exploration actions (compute,
analyse, transform, search, give, etc.) and nouns like data, dataset, data
collection, table, etc. The extracted vocabulary also contains synonyms to
enable fluent interaction. The sentences the user issues are tokenised to
search for keywords in particular verbs and nouns. Data exploration actions
are associated with one or several potential conversational patterns.

Every conversational pattern has a corresponding execution plan graph pattern
(see Figure 3). As shown in the figure, the data transformation and
preparation request described by pattern P1, is transformed into an execution
plan represented by a directed acyclic graph. A node in the plan can
correspond to an abstract exploration function, an action request of the bot
to the user and an action from the user.

\- Second strategy relies on using an existing chatbot API to deal with
complex conversations. The interpreted actions are then used for building the
execution plan that then guides the conversational exploration, guiding the
user to accomplish this task. This strategy is undergoing, and the objective
is to train the chat model with conversations to produce execution plans. The
execution of the plans with the chatbot ensuring the conversational
interaction can then assist users in exploring data collections intuitively.

To go beyond the exploration, a user would like to extract further
understanding of the data collection content: "I want to understand the
dataset’s content further". The bot proposes to compare different
classification techniques (Soofi and Awan, 2017): "Classification can be a
suitable technique to discover unseen patterns in your data collection. I can
perform different strategies. Do you want to have a try?" The execution plan
shown on the right side in figure 4 illustrates the non-resolved execution
plan. A first try can be to choose the K-means algorithm (Faber et al., 1994).
This choice launches several conversation patterns. The dotted nodes represent
potential tasks to be executed if the user selects to test further
classification techniques (e.g., SVM (Yue et al., 2003)).

Figure 4. Execution plan of a conversational data exploration pattern.

If the conversation is paused, the system stores the resolved plan with the
execution state of every task. Then, it can be retrieved and restarted as the
conversation is resumed. When the session is terminated, the system has the
execution log of the conversation and the exploration pipeline designed by the
user (intuitively).

##  4\. Exploring gender biases due to social norms

Our use case is inspired by the Human Development Report produced by the
United Nations Development Programme777https://hdr.undp.org. The report
proposed a Gender Social Norm Index (GSNI) to measure public attitudes towards
women across four dimensions (political, educational, economic, and physical
integrity) to assess how biased beliefs can impact gender equality and human
rights (Programme), 2023). The intention is to explore a dataset released in
2023 through conversational exploration to understand its content. The
analysis aims to compute metrics for many dimensions across different
countries and identify correlations of biases that impact gender inequality as
well as biases similarity across different countries. The focus is on the
conversational aspects and their connection with data processing.

World Values Survey (WVS) Dataset  assesses social, political, economic, and
cultural values and norms through questionnaires. The dataset contains
microdata captured in different waves and examines shifts in cultural values,
attitudes, and beliefs across countries and over time. The use case uses the
latest dataset contained in a 136.27 KB Excel file
888https://hdr.undp.org/sites/default/files/publications/additional-
files/2023-06/GSNI2023_AnnexTables2.xlsx produced on 12 January 2023..

Exploration conversations. This use case allowed for testing several
exploration patterns.
c Data preparation ( transformation, feature engineering, and quantitative
profile). The GSNI2023 file was uploaded in response to a user handshake
request: U1. "Help me to analyse my data". The request launches an instance of
the conversation pattern P1 shown in figure 4 (BX refers to a request produced
by the bot, UAX refers to an action done by the user, UX tags a user request):
— B1.  "Please upload your data collection." — UA1.  Upload file
— B2.  “Your collection is an Excel file with 5 sheets It must be transformed
into CSV. Do you want me to transform all sheets?” — U2. "Transform only the
first sheet."
3B. “We are going to start a data transformation process”
Chatin produces a transformed CSV file and a basic statistical description
(see the results produced by our system in the top side of Figure 5:(1)).
— U3.  "Analyse the linear correlation between each couple of numerical
attributes in the dataset".
Chatin produces a correlation matrix, showing the Pearson coefficient computed
for each couple of attributes as shown in Figure 5:2.
—- B4. "Are these results what you expected?" — —- U4. "Ok."
The final handshake includes the user’s feedback and a goodbye message from
the bot.

Figure 5. Chatin : A storytelling for the WVS Dataset.

\- [Test 2 composing meta-patterns P2, P3, and P5:] The conversation starts
with the user request "I want to understand the data further." (meta-pattern
P2). The chatbot proposes an explanation of the role and principle of
classification by the bot (meta-pattern P5). It suggests a first initiative
(with k-means, without telling the user) and launches a conversation for
collecting some data that serve as input to calibrate the analytics task. For
example, the chatbot says B1: "According to the characteristics of your data,
I have selected the numerical attributes. I have first removed correlated
attributes. Then I automatically determined the optimum number of groups to
classify the data. Based on the analysis, I should organise your data into 3
clusters. Here are the results." The Chatin produces the elbow plot and a 3-d
representation of the clustering with the corresponding centroids. According
to meta-pattern P3, the chatbot says B2: "Do you want me to explain the notion
of attributes correlation and how it is computed?". On acceptance of the user,
the chatbot explains: "Variable correlation is determined by computing the
Pearson coefficient. I decided to eliminate variables with a coefficient
greater than 0,95." (meta-pattern P5).

\- [Test 3 Proactive action P6:] The chatbot proactively generates
visualisation options with explanations so the user can provide feedback and
ask to adjust the result or try a different strategy. To conclude the session,
the system proposes a narrative (storytelling) of the whole conversation with
plots intended to allow a better understanding of the data. We do not show the
narrative here, but Figure 5 shows the plots it contains. The plot in Figure
5:5 shows clustering results on a world map, highlighting groups of countries
with similar biases. Because the dataset provides data for only a subset of
countries, the map shows countries in the world map for which data are
unavailable. To give more insight into the clustering results, Figure 5:6
shows each group’s centroids (in terms of average and standard deviation). The
user can see that the clustering provided consists of coherent and well-
separated groups of countries regarding the bias indices. As shown in Figure
5:(6), each group has a centroid characterised by values for all input data
(i.e., well-separated groups) that are very different from the values assumed
by the same input for the other centroids, while the standard deviation for
each input variable is often very low, showing that the identified groups are
very cohesive.

Assessment setting. One of our contributions is proposing a set of assessment
metrics for our approach that can go beyond interpreting user requests. Our
work is not willing to compete with existing very powerful chatbots. Our
contribution concerns the design of an intuitive data exploration process
where the guidance comes from the system and not the user, a priori non-DS
specialist. We propose the following assessment metrics:
[M1] The number of user-chatbot interactions the system requires for
identifying the user’s intention modelled by a meta-pattern.
[M2] Precision and recall of the execution plans.
[M3] Acceptability of the responses given by the number of liked feedback.
[M4] Data exploration task completion given by the number of sessions that
lead to the generation of storytelling.
[M5] Customer satisfaction metrics, such as Customer satisfaction score by
asking customers to rate their experience after an interaction with Chatin .
Net promoter score (it measures if customers would be willing to recommend
Chatin  to other people (Customers who give a score of 9 or 10 are called
promoters, from o tp 6 detractive and from 7 to 8 passive).
Scope and Limitations. We have tested our approach under a proof of concept
introduced in this section. We have also run tests exploring datasets from our
previous projects (Cerquitelli et al., 2020; Bethaz et al., 2021b). However,
the users have advanced DS knowledge even if they have other domain expertise.
This experience has allowed defining assessment metrics. Therefore, we are
currently setting two types of tests: (1) generating synthetical conversations
for testing our system for metrics M1 and M2; (2) organising groups of users
with absent, low and medium IT expertise to test M3, M4 and M5.

We envisioned a data exploration pipeline design where interactive,
conversational approaches empower users of all backgrounds and expertise
levels to explore data. Conversations must be agile, intuitive, and user-
friendly to achieve this goal. These conversations should be tailored to the
data and the user’s profile, guiding the user toward a clear understanding of
the data and the exploration tools available for their task.

##  5\. Conclusion and Future Work

This paper introduced Chatin , a conversational data exploration system
allowing users to design their pipelines. The system’s objective is to propose
an explorative and interactive design environment where users can understand
the content of data collections and produce a quantitative profile of their
content going back and forth in their analytics tasks. Once the exploration
converges, the system aggregates and synthesises the process into a
storytelling document.

Our future work aims to make the conversation flow more natural by
interpreting user requests and mapping them into actions considering the
data’s nature. We will also provide personalised answers, narratives, and
visualisations to deliver easily understandable data stories. Additionally, we
are working on predicting and recommending the next task in the data
exploration process based on previous actions and dataset characteristics.

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