Condensed Matter Physics, 2006, vol. 9, No. 2(46), p. 393-402, English

Title: A class of solvable models in Condensed Matter Physics
  F.Mancini (Dipartimento di Fisica "E.R. Caianiello" Laboratorio Regionale SuperMat, INFM Università degli Studi di Salerno, I-84081 Baronissi (SA), Italy)

In this paper, we show that there is a large class of fermionic systems for which it is possible to find, for any dimension, a finite closed set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of motion closes and analytical expressions for the Green's functions are obtained in terms of a finite number of parameters, to be self-consistently determined. Several examples are given. In particular, for these examples it is shown that in the one-dimensional case it is possible to derive by means of algebraic constraints a set of equations which allow us to determine the self-consistent parameters and to obtain a complete exact solution.

Key words: strongly correlated electron systems, Hubbard model, Ising model, exact solution
PACS: 71.10.-w, 71.10.Fd, 71.27.+a

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