Construction of density operator for a general mean-field Hamiltonian and its application to the models of correlated fermions

TL;DR

This paper develops a formalism to construct the density operator for mean-field lattice-fermion Hamiltonians, incorporating new terms that affect thermodynamics, especially in complex correlated fermion models.

Contribution

It introduces a consistent method to include local fugacities and molecular fields in the density operator for mean-field models, extending beyond traditional approximations.

Findings

The formalism modifies thermodynamic properties in correlated fermion models.

In some cases, the new terms are redundant, but they are essential for accurate descriptions in complex models.

Application to the renormalized t-J model shows nontrivial effects on thermodynamics.

Abstract

We analyze a class of mean-field (MF) lattice-fermion Hamiltonians and construct the corresponding grand-canonical density operator for such system. New terms are introduced, which may be interpreted as local fugacities, molecular fields, etc. The presence of such terms is an unavoidable consequence of a consistent statistical description. Although in some cases (e.g. in the Hartree or the Hartree-Fock-type approximation) the presented formalism is redundant, in general (e.g. for a renormalized t-J model) it leads to nontrivial modifications of the thermodynamic properties.