Segregation in the asymmetric Hubbard model

TL;DR

This paper investigates the asymmetric Hubbard model with spin-dependent hoppings, proving phase separation in the ground state under strong interactions and asymmetry, extending previous results from related models.

Contribution

It introduces a rigorous proof of phase separation in the asymmetric Hubbard model, expanding understanding of electron behavior in spin-dependent hopping systems.

Findings

Ground state exhibits phase separation away from half-filling

Phase separation occurs under strong interactions and sufficient asymmetry

Extends results from the Falicov-Kimball model to the asymmetric Hubbard model

Abstract

We study the `asymmetric' Hubbard model, where hoppings of electrons depend on their spin. For strong interactions and sufficiently asymmetric hoppings, it is proved that the ground state displays phase separation away from half-filling. This extends a recent result obtained with Freericks and Lieb for the Falicov-Kimball model. It is based on estimates for the sum of lowest eigenvalues of the discrete Laplacian in arbitrary domains.