Fermionic systems with charge correlations on the Bethe lattice

TL;DR

This paper analyzes a fermionic model with charge correlations on the Bethe lattice, revealing phase transitions and symmetry breaking, and compares it to an equivalent spin model with different physical behaviors.

Contribution

It provides an exact solution for the fermionic and spin models on the Bethe lattice, highlighting differences in their physical stability and phase behavior.

Findings

Existence of a critical temperature with symmetry breaking.

Fermionic system unstable against charge separation below T_c.

Spin system remains stable with homogeneous ferromagnetic phase.

Abstract

A fermionic model, built up of q species of localized Fermi particles, interacting by charge correlations, is isomorphic to a spin-q/2 Ising model. However, the equivalence is only formal and the two systems exhibit a different physical behavior. By considering a Bethe lattice with q=1, we have exactly solved the models. There exists a critical temperature below which there is a spontaneous breakdown of the particle-hole symmetry for the first model, and of the spin symmetry for the second. While the spin system is always stable and exhibits a homogeneous ferromagnetic phase below T_{c}, the fermionic system for T<T_{c} is unstable against the formation of inhomogeneous phases with charge separation.