Fermionic systems with charge correlationsF. Mancini
Dipartimento di Fisica "E. R. Caianiello" - Unità di ricerca INFM di Salerno Università degli Studi di Salerno - I-84081 Baronissi (SA), Italy
received 3 March 2005; accepted in final form 23 March 2005
published online 13 April 2005
In this paper, we show that a system of localized particles, satisfying the Fermi statistics and subject to finite-range interactions, can be exactly solved in any dimension. In fact, in this case it is always possible to find a finite closed set of eigenoperators of the Hamiltonian. Then, the hierarchy of the equations of motion for the Green's functions eventually closes and exact expressions for them are obtained in terms of a finite number of parameters. For example, the method is applied to the two-state model (equivalent to the spin-(1/2) Ising model) and to the three-state model (equivalent to the extended Hubbard model in the ionic limit or to the spin-1 Ising model). The models are exactly solved for any dimension d of the lattice. The parameters are self-consistently determined in the case of d=1.
71.10.-w - Theories and models of many-electron systems.
71.10.Fd - Lattice fermion models (Hubbard model, etc.).
71.27.+a - Strongly correlated electron systems; heavy fermions.
© EDP Sciences 2005