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abstract: 'The geometric phase can act as a signature for critical regions of interacting spin chains in the limit where the corresponding circuit in parameter space is shrunk to a point and the number of spins is extended to infinity; for finite circuit radii or finite spin chain lengths, the geometric phase is always trivial (a multiple of $2\pi$). In this work, by contrast, two related signatures of criticality are proposed which obey finite-size scaling and which circumvent the need for assuming any unphysical limits. They are based on the notion of the *Bargmann invariant* whose phase may be regarded as a discretized version of Berry’s phase. As circuits are considered which are composed of a discrete, finite set of vertices in parameter space, they are able to pass directly *through* a critical point, rather than having to circumnavigate it. The proposed mechanism is shown to provide a diagnostic tool for criticality in the case of a given non-solvable one-dimensional spin chain with nearest-neighbour interactions in the presence of an external magnetic field.'
author:
- 'Moritz E. Reuter'
- 'Michael J. Hartmann'
- 'Martin B. Plenio'
title: Geometric Phases and Critical Phenomena in a Chain of Interacting Spins
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