The split property and the symmetry breaking of the quantum spin chain

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Abstract

We consider the relationship between the symmetry breaking and the split property of pure states of quantum spin chains. We obtain a representation theoretic condition implying that the half-sided uniform mixing condition leads to symmetry breaking of translationally invariant pure states. This is a mathematical generalization of Dichotomy previously found by I. Affleck and E. Lieb and M. Aizenman and B. Nachtergaele for ground states of a special class of Hamiltonians.

Original languageEnglish
Pages (from-to)393-416
Number of pages24
JournalCommunications in Mathematical Physics
Volume218
Issue number2
DOIs
Publication statusPublished - Apr 1 2001

All Science Journal Classification (ASJC) codes

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

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