Geodesic
Invariant states for the time dynamics of a class of multidimensional lattice quantum Fermi systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 1, pp. 76-83 Cet article a éte moissonné depuis la source Math-Net.Ru

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The study of invariant states of fermionic lattice systems begun earlier is contined. Under the assumption that the time dynamics corresponds to a (formal) Hamiltonian $H_0$ and the invariant state $\varphi$ is a KMS state for some Hamiltonian $H$ [1], one-dimensional lattice Fermi systems were considered in the earlier work. In particular, the case when $H_0$ is not a quadratic form in the creation and annihilation operators and all nonquadratic terms in $H_0$ are diagonal was studied. In this case, it was shown that up to an arbitrary diagonal quadratic form $N$ the Hamiltonian $H$ is proportional to $H_0$, i. e., that $\varphi$ is a KMS state of $\beta H_0+ N$. In this paper, we obtain a similar result for Fermi systems of arbitrary dimension by a somewhat different method to the one used earlier [1]. 
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N. E. Ratanov; Yu. M. Sukhov. Invariant states for the time dynamics of a class of multidimensional lattice quantum Fermi systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 94 (1993) no. 1, pp. 76-83. http://geodesic.mathdoc.fr/item/TMF_1993_94_1_a5/

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