Spatially inhomogeneous phase in the two-dimensional repulsive Hubbard model

TL;DR

This study uses advanced quantum Monte Carlo methods to analyze the ground state properties of the 2D Hubbard model, revealing phase separation and the loss of antiferromagnetic order upon doping.

Contribution

It introduces improved techniques for reducing finite-size effects and accurately determining phase behavior in the 2D Hubbard model at intermediate interactions.

Findings

Evidence of phase separation into distinct density regions.

Long-range antiferromagnetic order is lost below a critical doping level.

Finite-size effects are significantly reduced by boundary condition integration.

Abstract

Using recent advances in auxiliary-field quantum Monte Carlo techniques and the phaseless approximation to control the sign/phase problem, we determine the equation of state in the ground state of the two-dimensional repulsive single-band Hubbard model at intermediate interactions. Shell effects are eliminated and finite-size effects are greatly reduced by boundary condition integration. Spin-spin correlation functions and structure factors are also calculated. In lattice sizes up to $16\times 16$, the results show signal for phase-separation. Upon doping, the system separates into one phase of density $n=1$ (hole-free) and the other at density $n_c$ ($\sim 0.9$). The long-range antiferromagnetic order is coupled to this process, and is lost below $n_c$.