On the Hartree-Fock phase diagram for the two-dimensional Hubbard model

TL;DR

This paper introduces an analytical approach to construct Hartree-Fock phase diagrams for the 2D Hubbard model, providing explicit formulas that improve accuracy and rigorously prove the existence of mixed phases.

Contribution

The paper develops a novel asymptotic analytical method for phase diagram construction, surpassing numerical approaches in precision and rigor for the 2D Hubbard model.

Findings

Derived explicit formulas for phase boundaries

Achieved high-accuracy agreement with numerical results

Provided the first rigorous proof of mixed phases

Abstract

We propose an analytical method for the construction of Hartree-Fock phase diagrams for the (fermion) Hubbard model and various generalizations thereof. Such phase diagrams are traditionally constructed numerically, but we argue that, by using asymptotic techniques, it is possible to obtain analytic formulas approximating the curves separating the different phases to very high accuracy. To illustrate the new method, we apply it to the two-dimensional Hubbard model on the square lattice at zero temperature. This yields formulas for the Hartree-Fock phase boundaries that agree with, but also improve on, earlier numerical results. In particular, our results provide the first rigorous proof of the existence of mixed phases in this model.