Invariant states for the time dynamics of a class of multidimensional lattice quantum Fermi systems (1993)
The study of invariant states of fermionic lattice systems begun earlier is contined. Under the assumption that the time dynamics corresponds to a (formal) HamiltonianH 0 and the invariant state ? is a KMS state for some “Hamiltonian”H [1], one-dimensional lattice Fermi systems were considered in the earlier work. In particular, the case whenH 0 is not a quadratic form in the creation and annihilation operators and all nonquadratic terms inH 0 are diagonal was studied. In this case, it was shown that up to an arbitrary diagonal quadratic formN the HamiltonianH is proportional toH 0, i.e., that ? is a KMS state of ?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].