body localization. We consider the following model:
\begin{align}
  H = J \sum_{i=1}^{L} \boldsymbol{S}_i\cdot\boldsymbol{S}_{i+1} + \sum_{\alpha=x,y,z}\sum_{i=1}^L h^\alpha_i S^\alpha_i,
  \label{eq:MBLmodel}
\end{align}
where $\boldsymbol{S}$ denote spin-$1/2$ operators. The local fields $h^\alpha_i$ are drawn from a uniform box distribution with zero mean and width $h^\alpha_{\textrm{max}}$. We set $h^x_{\textrm{max}} = h^z_{\textrm{max}} = h_{\textrm{max}}$ and $h^y_{\textrm{max}} = 0$. The disorder allows us to generate many samples at a fixed set of model parameters, in analogy to the different configurations for a fixed temperature in the classical spin systems \cite{Car16a, Wan16a}. 

The model in equation (\ref{eq:MBLmodel}) has a transition between thermalizing and non-thermalizing (i.e. many-body localized) behavior, driven by the disorder strength $h_{\textrm{max}}$. In particular, when varying $h_{\textrm{max}}$, both the energy level statistics as well as the statistics of the entanglement spectra change their nature \cite{Geraedts2016}. For the case of the energy levels, the gaps (level spacings) follow either a Wigner-Dyson distribution for the thermalizing phase,  or a Poisson distribution for the localized phase; while for the entanglement spectrum, the Wigner-Dyson distribution is replaced by a semi-Poisson distribution. Note that the change of ES can already be seen from the statistics in a \emph{single} eigenstate \cite{Geraedts2016}. 

We numerically obtain the entanglement spectrum for the groundstate of the model in equation (\ref{eq:MBLmodel}), for disorder strengths between $h_{\textrm{max}} = J$ and $h_{\textrm{max}} = 5J$. The transition was shown to happen around $h_{\textrm{max}} \approx 3J$ \cite{Geraedts2016}, but we stress that our method does not rely on this knowledge. We would simply have started from a larger width of points, and then systematically narrow it down to the current range. At each value of $h_{\textrm{max}}$ we generate $10^5$ disorder realizations for system size $L = 12$ and calculate the entanglement spectrum for $L_A=L_B=6$. These $2^6=64$ levels are used as the input to the NN. 

First, we try to use an unsupervised PCA to cluster the data. This analysis shows that the first two principal components are dominant, with the other components being of order $10^{-4}$ or less. However, a scatterplot of the data when projected onto the first two principal components (shown in Fig.~\ref{fig:MBLPCA}a) does not reveal a clear clustering of the spectra.



We therefore turn to train a shallow feedforward network on the entanglement spectra in order to use the confusion scheme. Here we use a network with 64 input neurons, 100 hidden neurons and 2 output neurons. The results are shown in Fig.~\ref{fig:MBLPerformance}b. Also in this case, the characteristic W-shape is obtained and we detect the transition at $h_c \approx 3J$. In addition to the previous cases, we also consider explicitly the performance of the network $\mathcal{N}_{h'_{c}}$ \emph{at} $h'_c$. We do this to confirm that the labelling with $h'_c$ at $3J$ is indeed correct. We expect namely that the training of the network is most robust against changes in its parameters for the correct labelling. In other words, we may also look for the $h'_c$ at which the training is most independent of chosen conditions. As shown in Fig.~\ref{fig:MBLPerformance}c, this point is also at $h'_c \approx 3J$.

\section{Discussion}
In this work we have explored the uses of machine learning in identifying (quantum) phase transitions from the overall performance of neural networks. As input data for training we proposed to use the entanglement spectrum of a quantum state, since it provides an excellent way of compressing the otherwise exponentially large wavefunction. We have shown that by confusing the neural network, by purposefully mislabelling the data, we are able to identify the phase transition between two phases of matter without prior knowledge of them. We demonstrated this for three different scenario's. We expect our method to be useful also in situations where it is not clear whether two phases are identical, or whether intervening phases exist in between other phases. If the underlying data in such situations has a (hidden) pattern that distinguishes them, our machine learning approach may well be able to find it. Our method is not limited to applications in condensed matter physics and phase transitions, but might prove useful in any field in which large amounts of data can be classified using a priori unknown labels. 

An interesting direction for future studies is the relaxation of the assumption that there are only two phases to be distinguished. If there are multiple phase transitions present in the data, the characteristic W-shape will be modified, and its new shape (i.e. the number of peaks) will signal the correct number of different labels. Additionally, it may be possible to formulate this method in a self-consistent way, with an adaptive labelling and having the algorithm determine the correct labels by itself. 

\section*{Acknowledgements}
E.v.N and S.H. gratefully acknowledge financial support from the Swiss National Science Foundation (SNSF). Y.-H.L. is supported by ERC Advanced Grant SIMCOFE. E.v.N. acknowledges fruitful discussions with Maciej Koch-Janusz on extending the confusion scheme to the case with multiple phases. E.v.N. and Y.-H.L. acknowledge helpful discussions with Giuseppe Carleo, Juan Osorio and Lei Wang. E.v.N and S.H. thank Andreas Krause for useful discussion on machine learning. \\

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Hello there! I wanted to make a post about some of my favorite cards that I made of 2017. It was a very busy year preparing for the wedding, so there was scrappin’ & craftin’ going on every where! Here’s my favorite:
I fell in love with Yana’s card (here). So, I made a similar version. Gracee’s valentine!
I created the 2016 for a scrap book I made for our Disney vacation. I love the Villains!
Dwen and I celebrated our 50th birthday and my Marvel lovin’ boy got this pop up card!
Lots of ballerina’s for Grace’s 5th birthday invites, Mario (on a wobbler) to celebrate Jagger’s 5th birthday and of course, Halloween!
This is the card I made for Brittany and Adam for their bridal shower. She loves personal touches…and the lower card is my first try at chibitronics. I made this card for Adam to give to Brittany on their wedding day. I was very please with how it turned out.
There you have it, my 10 faves. Let me know which one you like best! Thanks for stopping by! Have a good week! C~Together with your colleagues you will help our customers to achieve more, as a Azure Architect you are a key player for our deliveries. Your role is to suggest and design an architecture that maps customer needs and that also aligns with Microsoft roadmap. Apart from presenting solutions to our customers you also love to share knowledge with everyone, maybe you have a blog or usually express yourself and your ideas publicly for developing yourself and others.Дайте соответствующие существительные жен­ского рода.
Дайте соответствующие существительные муж­ск