Phase Separation in the Two-Dimensional Hubbard Model

TL;DR

This paper demonstrates that the two-dimensional Hubbard model on a square lattice does not exhibit phase separation at any filling level at finite temperature, aligning with quantum Monte Carlo results.

Contribution

It provides a somewhat exact proof ruling out phase separation in the 2D Hubbard model using known exact results and symmetry properties.

Findings

No phase separation at finite temperature for any filling

Consistent with quantum Monte Carlo calculations

Applicable to both attractive and repulsive interactions

Abstract

By making use of known exact results and symmetry properties for the one-band Hubbard model, we show in a somewhat exact manner that there is no phase separation on a square lattice at arbitrary fillings at finite temperature for both attractive and repulsive on-site Coulomb interaction. This result is consistent with the quantum Monto Carlo calculation.