Variational Monte Carlo studies of attractive Hubbard model I

TL;DR

This study uses variational Monte Carlo methods to analyze the normal states of the two-dimensional attractive Hubbard model, revealing a metal-insulator transition at a critical interaction strength and comparing different wave functions' effectiveness.

Contribution

It introduces an improved wave function incorporating intersite correlations and provides a detailed analysis of the metal-insulator transition in the attractive Hubbard model.

Findings

A clear crossover observed with the plain Gutzwiller wave function.

A metal-insulator transition occurs at |U|~W with an improved wave function.

Conventional Jastrow wave functions are less effective in capturing the transition.

Abstract

Normal states of the attractive Hubbard model, especially in two dimension, are studied in the light of a transition from a Fermi liquid to an insulating or gapped state. A series of variational Monte Carlo calculations with better statistics is carried out to estimate accurately expectation values by several many-body wave functions. Although a relatively clear crossover is observed even in the plain Gutzwiller wave function, the states in both regimes are metallic. Meanwhile, a substantial metal-insulator transition takes place at |U|\sim W (band width) in an improved wave function in which intersite correlation is introduced by taking account of virtual states in the second-order perturbation in the infinite-|U| limit. The critical value is favorably compared with recent results of the dynamical-mean-field approximation. In contrast, a conventional Jastrow-type wave functions scarcely improve the normal state. In addition, the issue of Brinkman-Rice metal-insulator transition is reconsidered with much larger systems.