Quantum Monte Carlo Study of a Dynamic Hubbard Model

TL;DR

This study uses determinant Quantum Monte Carlo to analyze a dynamic Hubbard model, revealing that coupling to a bosonic field can induce attractive pairing interactions and affect magnetic and insulating properties.

Contribution

First application of determinant Quantum Monte Carlo to the dynamic Hubbard model showing how bosonic coupling influences pairing and magnetic correlations.

Findings

Extended s-wave pairing vertex becomes attractive with increased bosonic coupling

Antiferromagnetic correlations and Mott gap are stabilized near half-filling

Energy shows near linear dependence on particle density indicating phase separation tendency

Abstract

The `dynamic' Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repulsion is modulated by a coupling to a fluctuating bosonic field. We investigate one such model, introduced by Hirsch, using the determinant Quantum Monte Carlo method. Our key result is that the extended s-wave pairing vertex, repulsive in the usual static Hubbard model, becomes attractive as the coupling to the fluctuating Bose field increases. The sign problem prevents us from exploring a low enough temperature to see if a superconducting transition occurs. We also observe a stabilization of antiferromagnetic correlations and the Mott gap near half-filling, and a near linear behavior of the energy as a function of particle density which indicates a tendency toward phase separation.