Eur. Phys. J. B 73, 581-595 (2010)
https://doi.org/10.1140/epjb/e2010-00031-8

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

¹ Dipartimento di Fisica “E. R. Caianiello", Università degli Studi di Salerno, Via Ponte don Melillo, 84084 Fisciano (SA), Italy
² Unità CNISM di Salerno, Via Ponte don Melillo, 84084 Fisciano (SA), Italy
³ Laboratorio Regionale SuperMat, CNR-INFM, Via Ponte don Melillo, 84084 Fisciano (SA), Italy
⁴ I.N.F.N. Sezione di Perugia, Via A. Pascoli, 06123 Perugia, Italy

Corresponding author: fpmancini@sa.infn.it

Received: 28 September 2009
Revised: 30 November 2009
Published online: 27 January 2010

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.