Solution of the "sign problem" for the half filled Hubbard-Holstein model

TL;DR

This paper introduces a sign-free path integral formulation for the half-filled Hubbard-Holstein model, enabling efficient simulations and revealing a region without magnetic or charge order between quantum critical points.

Contribution

It presents a novel method to eliminate the sign problem in the Hubbard-Holstein model at half-filling using auxiliary fields and exact phonon integration.

Findings

Extended region without magnetic or charge order near U ≈ g^2/ω_0

Quantum critical points at zero temperature

Potential for studying strongly correlated models without sign issues

Abstract

We show that, by an appropriate choice of auxiliary fields and exact integration of the phonon degrees of freedom, it is possible to define a 'sign-free' path integral for the so called Hubbard-Holstein model at half-filling. We use a statistical method, based on an accelerated and efficient Langevin dynamics, for evaluating all relevant correlation functions of the model. Preliminary calculations at $U/t=4$ and $U/t=1$, for $\omega_0/t=1$, indicate a quite extended region around $U \simeq {g^2 \over \omega_0}$ without either antiferromagnetic or charge-density-wave orders, separating two quantum critical points at zero temperature. The elimination of the sign problem in a model without explicit particle-hole symmetry may open new perspectives for strongly correlated models, even away from the purely attractive or particle-hole symmetric cases.