On Fermion Grading Symmetry for Quasi-Local Systems |
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Authors: | Hajime Moriya |
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Institution: | (1) Department of Mathematics, Graduate School of Science, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-0810, Japan |
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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. |
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