On relative bounds for interacting Fermion operators

Abstract

We consider a system of interacting fermions whose Hamiltonian is unitarily transformed so that the interaction is a quartic perturbation of the Hartree–Fock effective Hamiltonian. It is shown under natural model assumptions that the interaction does not admit a relative bound with respect to the effective Hamiltonian that is uniform in the system’s size.

This bound is exemplified on the 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 $L$.