Ising phase transitions and thermodynamics of correlated fermions in a two-dimensional spin-dependent lattice potential

TL;DR

This study uses numerically exact quantum Monte Carlo methods to analyze phase transitions and thermodynamics in a two-dimensional spin-dependent Hubbard model, revealing precise transition temperatures and thermodynamic behaviors relevant to optical lattice experiments.

Contribution

It provides highly accurate, sign-problem-free quantum Monte Carlo results for the Hubbard model with spin-dependent anisotropic hopping, including transition temperatures and thermodynamic properties.

Findings

Identified Ising-type antiferromagnetic and charge-density wave orders at finite temperatures.

Mapped entropy and correlations relevant for optical lattice experiments.

Explored sign problem behavior and possible stripe order away from half filling.

Abstract

We present a {\it numerically exact} study of the Hubbard model with spin-dependent anisotropic hopping on the square lattice using auxiliary-field quantum Monte Carlo method. At half filling, the system undergoes Ising phase transitions upon cooling, leading to the formation of Ising-type antiferromagnetic order for repulsive interactions and charge-density wave order for attractive interactions at finite temperatures. By elegantly implementing the sign-problem-free condition and Hubbard-Stratonovich transformations, we achieve significant improvements in precision control of the numerical calculations and obtain highly accurate results of the transition temperatures from weak to strong interactions across representative anisotropies. We further characterize the system by examining the temperature dependence of various thermodynamic properties, including the energy, double occupancy, specific heat and charge susceptibility. Specifically, we provide unbiased numerical results of the entropy map on temperature-interaction plane, the critical entropy, and the spin, singlon and doublon correlations, all of which are directly measurable in optical lattice experiments. Away from half filling, we explore the behavior of the sign problem and investigate the possible emergence of stripe spin-density wave order in the system with repulsive interaction.