Affordable Access

deepdyve-link deepdyve-link
Publisher Website

Geometric Phases and Critical Phenomena in a Chain of Interacting Spins

Authors
  • Reuter, M. E.
  • Hartmann, M. J.
  • Plenio, M. B.
Type
Published Article
Publication Date
Dec 22, 2006
Submission Date
Dec 22, 2006
Identifiers
DOI: 10.1098/rspa.2007.1822
arXiv ID: quant-ph/0612194
Source
arXiv
License
Unknown
External links

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 2pi). 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.

Report this publication

Statistics

Seen <100 times