On fermion grading symmetry for quasi-local systems

Hajime Moriya

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We discuss fermion grading symmetry for quasi-local systems with graded commutation relations. We introduce a criterion of spontaneously symmetry breaking (SSB) for general quasi-local systems. It is formulated based on the idea that each pair of distinct phases (appeared in spontaneous symmetry breaking) should be disjoint not only for the total system but also for every complementary outside system of a local region specified by the given quasi-local structure. Under a completely model independent setting, we show the absence of SSB for fermion grading symmetry in the above sense. We obtain some structural results for equilibrium states of lattice systems. If there would exist an even KMS state for some even dynamics that is decomposed into noneven KMS states, then those noneven states inevitably violate our local thermal stability condition.

Original languageEnglish
Pages (from-to)411-426
Number of pages16
JournalCommunications in Mathematical Physics
Volume264
Issue number2
DOIs
Publication statusPublished - 2006 Jun
Externally publishedYes

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broken symmetry
fermions
symmetry
commutation
thermal stability

ASJC Scopus subject areas

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

Cite this

On fermion grading symmetry for quasi-local systems. / Moriya, Hajime.

In: Communications in Mathematical Physics, Vol. 264, No. 2, 06.2006, p. 411-426.

Research output: Contribution to journalArticle

Moriya, Hajime. / On fermion grading symmetry for quasi-local systems. In: Communications in Mathematical Physics. 2006 ; Vol. 264, No. 2. pp. 411-426.
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