Fermionic systems with charge correlations

TL;DR

This paper presents an exact solution method for fermionic systems with charge correlations, applicable in any dimension, by identifying a finite set of eigenoperators that close the equations of motion for Green's functions.

Contribution

It introduces a novel exact solution approach for localized fermionic systems with finite-range interactions in arbitrary dimensions.

Findings

Exact solutions for two-state and three-state models in any dimension

Method applies to models equivalent to spin-1/2 and spin-1 systems

Parameters are self-consistently determined in one-dimensional case

Abstract

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.