Update of Hartree--Fock theory for Hubbard-like models

TL;DR

This paper updates Hartree--Fock theory for Hubbard-like models by introducing a stability test that accurately identifies mixed phases and corrects previous misconceptions in condensed matter physics.

Contribution

It presents a new stability test for Hartree--Fock solutions, enabling reliable detection of mixed phases and translation symmetry breaking in Hubbard-like models.

Findings

Mixed phases are common in Hubbard-like models across dimensions.

The stability test reveals regions with coexisting phases.

Previous results in literature are qualitatively incorrect without this update.

Abstract

We show that the standard textbook description of (restricted) Hartree--Fock theory for (Fermi) Hubbard-like models is in need of an update, and we present such an update allowing us to correct basic and established results in the condensed matter physics literature that are qualitatively wrong. Our update amounts to adding a test which reliably checks the thermodynamic stability of solutions of Hartree--Fock equations. This stability test makes it possible to detect, by simple means and with certainty, regions in phase space where the model exhibits mixed phases where two conventional phases coexist and translation invariance is broken in complicated ways; in such a mixed phase, unconventional physics is to be expected. Our results show that mixed phases are ubiquitous in Hubbard-like models in arbitrary dimensions.