Different orderings in the narrow-band limit of the extended Hubbard model on the Bethe lattice

TL;DR

This paper provides an exact solution for the extended Hubbard model on a Bethe lattice, analyzing phase diagrams with various interactions and revealing regions of charge order and phase separation.

Contribution

It offers a comprehensive analytical solution to the extended Hubbard model in the atomic limit on a Bethe lattice, including finite temperature phase diagrams.

Findings

Identification of critical regions with charge ordering and phase separation.

Analysis of thermodynamic quantities supporting phase diagram features.

Exact solution applicable to both repulsive and attractive interactions.

Abstract

We present the exact solution of a system of Fermi particles living on the sites of a Bethe lattice with coordination number z and interacting through on-site U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the atomic limit. Within the Green's function and equations of motion formalism, we provide a comprehensive analysis of the model and we study the phase diagram at finite temperature in the whole model's parameter space, allowing for the on-site and nearest-neighbor interactions to be either repulsive or attractive. We find the existence of critical regions where charge ordering (V>0) and phase separation (V<0) are observed. This scenario is endorsed by the study of several thermodynamic quantities.