Quantum Monte Carlo study of mass-imbalanced Hubbard models

TL;DR

This paper introduces two new continuous-time quantum Monte Carlo methods to efficiently simulate mass-imbalanced Hubbard models, addressing the fermion sign problem and enabling studies of magnetic correlations and phase transitions.

Contribution

The authors develop and present solutions to the fermion sign problem for mass-imbalanced Hubbard models, along with algorithms for efficient simulations on bipartite lattices.

Findings

Dependence of spin correlation on mass imbalance in 1D

Observation of thermal and quantum phase transitions in 2D

Unbiased predictions relevant for ultracold atom experiments

Abstract

Building on recent solutions of the fermion sign problem for specific models we present two continuous-time quantum Monte Carlo methods for efficient simulation of mass-imbalanced Hubbard models on bipartite lattices at half-filling. For both methods we present the solutions to the fermion sign problem and the algorithms to achieve efficient simulations. As applications, we calculate the dependence of the spin correlation on the mass imbalance in a one-dimensional lattice and study the thermal and quantum phase transitions to an antiferromagnetic Ising long-range ordered state in two dimensions. These results offer unbiased predictions for experiments on ultracold atoms and bridge known exact solutions of Falicov-Kimball model and previous studies of the SU(2)-symmetric Hubbard model.