On Relative Bounds for Interacting Fermion Operators

TL;DR

This paper investigates the bounds of effective interactions in a Hubbard model near its Hartree-Fock ground state, revealing that such bounds are not uniform as the system size increases.

Contribution

It provides the first analysis of relative bounds for interacting fermion operators in a lattice model, highlighting limitations in uniform bounds with system size.

Findings

No uniform relative bounds in system size L.

Effective interaction bounds depend on system size.

Insights into fermionic operator behavior in lattice models.

Abstract

We consider a Hubbard model with nearest neighbor interaction on a discrete $d$-dimensional torus of length $L$ around its Hartree-Fock ground state and derive relative bounds of the effective interaction with respect to the effective kinetic energy. It is shown that there are no relative bounds uniform in $L$.