Variational Monte Carlo analysis of the Hubbard model with a confining potential: one-dimensional fermionic optical lattice systems

TL;DR

This paper introduces an efficient variational Monte Carlo method to analyze the ground state properties of the one-dimensional Hubbard model with a confining potential, capturing metallic and Mott insulating coexistence.

Contribution

It combines variational Monte Carlo with a stochastic reconfiguration scheme to effectively study site-dependent correlations in confined Hubbard systems.

Findings

Successfully describes coexistence of metallic and Mott insulating regions

Demonstrates the method's efficiency in treating ground state properties

Addresses potential improvements of trial states

Abstract

We investigate the one-dimensional Hubbard model with a confining potential, which may describe cold fermionic atoms trapped in an optical lattice. Combining the variational Monte Carlo simulations with the new stochastic reconfiguration scheme proposed by Sorella, we present an efficient method to systematically treat the ground state properties of the confined system with a site-dependent potential. By taking into account intersite correlations as well as site-dependent on-site correlations, we are able to describe the coexistence of the metallic and Mott insulating regions, which is consistent with other numerical results. Several possible improvements of the trial states are also addressed.