Quantum Monte Carlo Study of the Disordered Attractive Hubbard Model

TL;DR

This study uses quantum Monte Carlo simulations to analyze the superconductor-insulator transition in a disordered attractive Hubbard model, revealing how disorder suppresses superconductivity and induces an insulating phase.

Contribution

It provides a detailed numerical investigation of the disorder-driven superconductor-insulator transition using determinantal quantum Monte Carlo methods, including analysis of various correlation functions and conductivity behavior.

Findings

Superfluid stiffness vanishes at critical disorder.

Charge and optical conductivities indicate transition from superconducting to insulating phase.

Temperature-dependent conductivity shows distinct metallic and insulating behaviors.

Abstract

We investigate the disorder-driven superconductor to insulator quantum phase transition (SIT) in an interacting fermion model using determinantal quantum Monte Carlo (QMC) methods. The disordered superconductor is modeled by an attractive Hubbard model with site disorder chosen randomly from a uniform distribution. The superconducting state which exists for small disorder is shown to evolve into an insulating phase beyond a critical disorder. The transition is tracked by the vanishing of (a) the superfluid stiffness, and (b) the charge stiffness or the delta function peak in the optical conductivity at zero frequency. We also show the behavior of the charge, spin, pair, and current correlations in the presence of disorder. Results for the temperature dependence of the dc conductivity, obtained by an approximate analytic continuation technique, are also presented both in the metallic phase above $T_c$ and the insulating phase. We discuss some of the complications in extracting the resistance at the transition point.