Stability of Insulating Phases in the Hubbard Model: a Cluster Expansion

TL;DR

This paper investigates the stability of insulating phases in the Hubbard model using a cluster expansion approach, providing bounds on Green's function decay length based on hopping rate and interaction strength.

Contribution

It introduces a cluster expansion method for analyzing Green's functions in the Hubbard model and derives bounds on the decay length related to model parameters.

Findings

Upper bound for expansion terms depending on hopping rate and interaction strength

Bound on decay length of Green's function established

Insulating regime stability characterized by exponential decay

Abstract

The stability of the insulating regime of the Hubbard model on a $d$-dimensional lattice, which is characterized by an exponential decay of the Green's functions, is investigated in terms of a cluster expansion. This expansion for the Green's function is organized in terms of connected clustered transfer matrices. An upper bound for the expansion terms is derived for the hopping rate ${\bar t}$ depending on the coupling constant $U$ as ${\bar t}<U/4d$. This implies an upper bound for the decay length of the Green's function.