Bilayer Hubbard model: Analysis based on the fermionic sign problem

TL;DR

This paper uses the average sign in quantum Monte Carlo simulations to clarify the phase diagram of the bilayer Hubbard model, revealing metallic regimes and a crossover to a band insulator at strong interactions.

Contribution

It introduces a novel application of the average sign metric to resolve open questions about the phase diagram of the bilayer Hubbard model.

Findings

Identification of finite-sized metallic regimes at small U.

Discovery of a crossover from correlated to uncorrelated band insulator at strong U.

Demonstration of the method's versatility in revealing physical properties.

Abstract

The bilayer Hubbard model describes the antiferromagnet to spin singlet transition and, potentially, aspects of the physics of unconventional superconductors. Despite these important applications, significant aspects of its `phase diagram' in the interplane hopping $t_\perp$ versus on-site interaction $U$ parameter space, at half filling, are largely in disagreement. Here we provide an analysis making use of the average sign of weights over the course of the importance sampling in quantum Monte Carlo simulations to resolve several central open questions. Specifically, this metric of the weights clarifies the finite-sized metallic regimes at small $U$. Furthermore, at strong interactions, it points to the existence of a crossover from a correlated to uncorrelated band insulator not yet explored in a variety of existing, unbiased numerical methods. Our work demonstrates the versatility of using properties of the weights in quantum Monte Carlo simulations to reveal important physical characteristics of the models under study.