Determinant Monte Carlo for the Hubbard Model with Arbitrarily Gauged Auxiliary Fields

Abstract

Monte Carlo methods for the Hubbard model rely on a Hubbard-Stratonovich (HS) decomposition (auxiliary field method) to perform importance sampling on classical variables. Freedom in the choice of the local HS fields can be formally seen as a gauge choice. While the choice of gauge does not influence observable quantities, it may influence intermediate quantities in the calculation, such as the famous “fermion sign”, and it may also influence the efficiency with which the algorithm explores phase space. The effect of arbitrary gauge choices on both aspects of the algorithm are investigated. It is found that in the single spin-flip determinantal approach, certain gauges lead to a better exploration of phase space. This improvement is demonstrated, in the intermediate coupling regime, by histograms which for the first time show the behavior expected from grand canonical simulations. It is also found that the improved phase space exploration can in practice offset the apparent disadvantage of a smaller fermion sign.