The extended Hubbard model in the ionic limit

TL;DR

This paper analyzes the extended Hubbard model in the ionic limit, revealing its isomorphism to a spin-1 Ising model, and provides exact solutions for eigenoperators, Green's functions, and correlation functions, especially in one dimension.

Contribution

It establishes a complete set of eigenoperators and eigenvalues for the model across dimensions and derives exact solutions in one dimension using algebraic constraints.

Findings

Exact solutions for 1D model properties

Closure of equations of motion for any dimension

Analytical expressions for Green's and correlation functions

Abstract

In this paper, we study the Hubbard model with intersite Coulomb interaction in the ionic limit (i.e. no kinetic energy). It is shown that this model is isomorphic to the spin-1 Ising model in presence of a crystal field and an external magnetic field. We show that for such models it is possible to find, for any dimension, a finite complete set of eigenoperators and eigenvalues of the Hamiltonian. Then, the hierarchy of the equations of motion closes and analytical expressions for the relevant Green's functions and correlation functions can be obtained. These expressions are formal because these functions depend on a finite set of unknown parameters, and only a set of exact relations among the correlation functions can be derived. In the one-dimensional case we show that by means of algebraic constraints it is possible to obtain extra equations which close the set and allow us to obtain a complete exact solution of the model. The behavior of the relevant physical properties for the 1D system is reported.