Geometric phases and critical phenomena in a chain of interacting spins

Moritz E. Reuter*, Michael J. Hartmann, Martin B. Plenio

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)


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 2π). In this work, 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 the Berry 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.

Original languageEnglish
Pages (from-to)1271-1285
Number of pages15
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2081
Publication statusPublished - 8 May 2007


  • Bargmann invariant
  • Berry phase
  • Criticality
  • Quantum phase transition
  • Spin chain

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering
  • General Physics and Astronomy


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