Condensed Matter Physics, 2006, vol. 9, No. 2(46), p. 393402, English
DOI:10.5488/CMP.9.2.393
Title:
A class of solvable models in Condensed Matter Physics
Author(s):
 F.Mancini
(Dipartimento di Fisica "E.R. Caianiello" Laboratorio
Regionale SuperMat, INFM Università degli Studi di Salerno,
I84081 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 selfconsistently
determined. Several examples are given. In particular, for these
examples it is shown that in the onedimensional case it is possible
to derive by means of algebraic constraints a set of equations which
allow us to determine the selfconsistent 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
