Exact solution of the extended Hubbard model in the atomic limit on the Bethe Lattice

TL;DR

This paper provides an exact solution for the extended Hubbard model in the atomic limit on the Bethe lattice, revealing phase transitions and re-entrant behavior at finite temperatures.

Contribution

It offers an exact analytical solution to the extended Hubbard model in the atomic limit on the Bethe lattice using equations of motion.

Findings

Identification of a phase transition to a broken particle-hole symmetry state at half filling.

Re-entrant behavior of the critical temperature as a function of model parameters.

Exact phase diagram characterization for the model.

Abstract

We study the phase diagram at finite temperature of a system of Fermi particles on the sites of the Bethe lattice with coordination number z and interacting through onsite U and nearest-neighbor V interactions. This is a physical realization of the extended Hubbard model in the atomic limit. By using the equations of motion method, we exactly solve the model. For an attractive intersite potential, we find, at half filling, a phase transition towards a broken particle-hole symmetry state. The critical temperature, as a function of the relevant parameters, has a re-entrant behavior as already observed in the equivalent spin-1 Ising model on the Bethe lattice.