Quantum Monte Carlo study of the metal-insulator crossover in the square-lattice Hubbard model

TL;DR

This study uses unbiased quantum Monte Carlo simulations to map the temperature-interaction phase diagram of the square-lattice Hubbard model, revealing an extended 'Bad Metal' crossover regime between Fermi liquid and Mott insulator phases.

Contribution

It provides the first detailed, unbiased numerical analysis of the metal-insulator crossover in the square-lattice Hubbard model at finite temperatures, including thermodynamic and spectral properties.

Findings

Identification of an extended crossover 'Bad Metal' regime.

Observation of nodal-antinodal dichotomy in spectral functions.

Mapping of thermal entropy and Pomeranchuk cooling regions.

Abstract

The interaction-driven evolution from a Fermi liquid to a Mott insulator is a hallmark of strongly correlated fermion systems. In this work, we present a {\it numerically unbiased} study of such metal-to-insulator crossover in the half-filled square-lattice Hubbard model at finite temperatures, employing auxiliary-field quantum Monte Carlo method. By jointly analyzing thermodynamic and dynamical observables, we establish the crossover diagram of the model in the temperature-interaction ($T$-$U$) plane. With increasing $U$, our numerical results reveal an extended crossover regime, which we refer to as the {\it Bad Metal}, that separates the Fermi liquid and Mott insulator. During the crossover, we also examine the antiferromagnetic spin correlations and observe pronounced nodal-antinodal dichotomy in the momentum-resolved single-particle spectral functions. Furthermore, we investigate the temperature dependence of several commonly used observables in the model. As representative results, we achieve an accurate map of the thermal entropy across the crossover diagram, and identify the parameter regions in which the model exhibits the Pomeranchuk cooling, characterized by an adiabatic cooling with increasing $U$. Beyond offering a more refined understanding of the crossover phenomenon, our work also provides valuable benchmark and guideline for future optical lattice experiments on the square-lattice Hubbard model.