Phase separation in the 2D Hubbard model: a fixed-node quantum Monte Carlo study

TL;DR

This study uses fixed-node quantum Monte Carlo to investigate phase separation in large 2D Hubbard models, suggesting potential phase separation near half-filling but highlighting the need for more accurate nodes and larger lattices for confirmation.

Contribution

First large-scale fixed-node quantum Monte Carlo study of phase separation in the 2D Hubbard model across various densities and interaction strengths.

Findings

Indications of phase separation near half-filling.

Hole-rich phase density decreases with increasing U.

Fixed-node bias limits definitive conclusions.

Abstract

Fixed-node Green's function Monte Carlo calculations have been performed for very large 16x6 2D Hubbard lattices, large interaction strengths U=10,20, and 40, and many (15-20) densities between empty and half filling. The nodes were fixed by a simple Slater-Gutzwiller trial wavefunction. For each value of U we obtained a sequence of ground-state energies which is consistent with the possibility of a phase separation close to half-filling, with a hole density in the hole-rich phase which is a decreasing function of U. The energies suffer, however, from a fixed-node bias: more accurate nodes are needed to confirm this picture. Our extensive numerical results and their test against size, shell, shape and boundary condition effects also suggest that phase separation is quite a delicate issue, on which simulations based on smaller lattices than considered here are unlikely to give reliable predictions.