Analyticity in Hubbard models

TL;DR

This paper rigorously proves the conditions under which the free energy of Hubbard and similar lattice models remains analytic, ensuring stability and clustering of the Gibbs state in the thermodynamic limit.

Contribution

It establishes rigorous conditions for analyticity, stability, and clustering of the Gibbs state in Hubbard models and general Hamiltonians with local interactions.

Findings

Free energy is analytic when eta t is small in Hubbard models.

Gibbs state exists, is exponentially clustering, and thermodynamically stable.

Results apply to a broad class of models with local Hamiltonian terms.

Abstract

The Hubbard model describes a lattice system of quantum particles with local (on-site) interactions. Its free energy is analytic when \beta t is small, or \beta t^2/U is small; here, \beta is the inverse temperature, U the on-site repulsion and t the hopping coefficient. For more general models with Hamiltonian H = V + T where V involves local terms only, the free energy is analytic when \beta ||T|| is small, irrespectively of V. The Gibbs state exists in the thermodynamic limit, is exponentially clustering and thermodynamically stable. These properties are rigorously established in this paper.