### Abstract

We consider Fermion systems on integer lattices. We establish the existence of dynamics for a class of long range interactions. The infinite volume ground states are considered. The equivalence of the variational principle and ground state conditions is proved for long range interactions. We also prove that any pure translationally invariant ground state of the gauge invariant algebra is extendible to a ground state of the full CAR algebra for the Hamiltonian with a chemical potential (equivalence of ensemble for canonical and ground canonical states at the zero temperature).

Original language | English |
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Pages (from-to) | 723-751 |

Number of pages | 29 |

Journal | Communications in Mathematical Physics |

Volume | 182 |

Issue number | 3 |

DOIs | |

Publication status | Published - Jan 1 1996 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*182*(3), 723-751. https://doi.org/10.1007/BF02506423

**Ground states of Fermions on lattices.** / Matsui, Taku.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 182, no. 3, pp. 723-751. https://doi.org/10.1007/BF02506423

}

TY - JOUR

T1 - Ground states of Fermions on lattices

AU - Matsui, Taku

PY - 1996/1/1

Y1 - 1996/1/1

N2 - We consider Fermion systems on integer lattices. We establish the existence of dynamics for a class of long range interactions. The infinite volume ground states are considered. The equivalence of the variational principle and ground state conditions is proved for long range interactions. We also prove that any pure translationally invariant ground state of the gauge invariant algebra is extendible to a ground state of the full CAR algebra for the Hamiltonian with a chemical potential (equivalence of ensemble for canonical and ground canonical states at the zero temperature).

AB - We consider Fermion systems on integer lattices. We establish the existence of dynamics for a class of long range interactions. The infinite volume ground states are considered. The equivalence of the variational principle and ground state conditions is proved for long range interactions. We also prove that any pure translationally invariant ground state of the gauge invariant algebra is extendible to a ground state of the full CAR algebra for the Hamiltonian with a chemical potential (equivalence of ensemble for canonical and ground canonical states at the zero temperature).

UR - http://www.scopus.com/inward/record.url?scp=0030569489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030569489&partnerID=8YFLogxK

U2 - 10.1007/BF02506423

DO - 10.1007/BF02506423

M3 - Article

AN - SCOPUS:0030569489

VL - 182

SP - 723

EP - 751

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 3

ER -