Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model

TL;DR

This study uses determinant quantum Monte Carlo to explore the two-dimensional Hubbard-Holstein model, revealing how electron-phonon interactions influence magnetic and charge orders and the fermion sign behavior.

Contribution

It provides detailed methodology for simulating the model and uncovers conditions where the fermion sign problem is mitigated, enabling studies of correlated polarons.

Findings

Fermion sign recovers at large Holstein coupling despite strong Hubbard interactions.

Evidence of competition between charge-density-wave and antiferromagnetic order at half-filling.

Methodology for treating lattice degrees of freedom in DQMC simulations.

Abstract

We have performed numerical studies of the Hubbard-Holstein model in two dimensions using determinant quantum Monte Carlo (DQMC). Here we present details of the method, emphasizing the treatment of the lattice degrees of freedom, and then study the filling and behavior of the fermion sign as a function of model parameters. We find a region of parameter space with large Holstein coupling where the fermion sign recovers despite large values of the Hubbard interaction. This indicates that studies of correlated polarons at finite carrier concentrations are likely accessible to DQMC simulations. We then restrict ourselves to the half-filled model and examine the evolution of the antiferromagnetic structure factor, other metrics for antiferromagnetic and charge-density-wave order, and energetics of the electronic and lattice degrees of freedom as a function of electron-phonon coupling. From this we find further evidence for a competition between charge-density-wave and antiferromagnetic order at half-filling.