Geometric Algorithm for Abelian-Gauge Models

TL;DR

This paper introduces a geometric simulation algorithm for abelian gauge models that mitigates ergodicity issues and shows promising efficiency and autocorrelation properties compared to traditional methods.

Contribution

The authors develop a geometric algorithm based on strong coupling expansion for abelian gauge models, demonstrating its practicality and potential advantages over standard algorithms.

Findings

Comparable efficiency to heat-bath algorithm in U(1) models

Avoids ergodicity problems caused by vortices

Hints of improved autocorrelation time behavior at critical points

Abstract

Motivated by the sign problem in several systems, we have developed a geometric simulation algorithm based on the strong coupling expansion which can be applied to abelian pure gauge models. We have studied the algorithm in the U(1) model in 3 and 4 dimensions, and seen that it is practical and is similarly efficient to the standard heat-bath algorithm, but without the ergodicity problems which comes from the presence of vortices. We have also applied the algorithm to the Ising gauge model at the critical point, and we find hints of a better asymptotic behaviour of the autocorrelation time, which therefore suggests the possibility of a smaller dynamical critical exponent with respect to the standard heat-bath algorithm.