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 language | English |
|---|---|
| Pages (from-to) | 411-426 |
| Number of pages | 16 |
| Journal | Communications in Mathematical Physics |
| Volume | 264 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2006 Jun |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - On fermion grading symmetry for quasi-local systems
AU - Moriya, Hajime
PY - 2006/6
Y1 - 2006/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=33645961311&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=33645961311&partnerID=8YFLogxK
U2 - 10.1007/s00220-006-1550-7
DO - 10.1007/s00220-006-1550-7
M3 - Article
AN - SCOPUS:33645961311
VL - 264
SP - 411
EP - 426
JO - Communications in Mathematical Physics
JF - Communications in Mathematical Physics
SN - 0010-3616
IS - 2
ER -