Determinant quantum Monte Carlo for the half-filled Hubbard model with nonlocal density-density interactions

TL;DR

This paper introduces a sign-problem-free determinant quantum Monte Carlo method for the half-filled Hubbard model with nonlocal interactions, enabling systematic study of its phase diagram and providing benchmarks for future research.

Contribution

A novel formalism for determinant quantum Monte Carlo that handles nonlocal interactions without sign problem for certain parameters, allowing detailed phase diagram analysis.

Findings

Identified antiferromagnetic phase for large positive U

Observed charge density wave for negative U and V

Detected s-wave superconductivity for negative U with small negative V

Abstract

We design a novel formalism of determinant quantum Monte Carlo method for the half-filled Hubbard model with on-site Hubbard interaction $U$ and nearest neighbor density-density interaction $V$ on the square lattice. The formalism is free of sign problem for $|U|\ge 4|V|$, and is achieved by introducing discrete auxiliary fields on the nearest-neighbor bonds alone. Based on this formalism, we study the ground state phase diagram of the model systematically using the projector algorithm. Within the sign-problem free parameter space $|U|\ge 4|V|$, we obtain antiferromagnetism for $U\ge 4|V|>0$, charge density wave for $U<-4V$ and $V>0$, s-wave superconductivity for $U<0$ and small negative $V$, and phase separation for $U<0$ and a larger negative $V$. We also obtain the single particle gap and spin excitation spectra, and by comparison to mean field results, as well as available literatures, we discuss the possible phase boundary beyond the sign-problem free region. The unbiased numerically exact results can be taken as benchmarks in future studies. Finally, we discuss possible extension for longer-range interactions in the model.