Exponential reduction of the sign problem at finite density in the 2+1D XY model via contour deformations

TL;DR

This paper demonstrates an exponential reduction of the sign problem in the 2+1D XY model at finite density by using contour deformations, enabling more efficient numerical simulations.

Contribution

The authors introduce a novel contour deformation method that significantly alleviates the sign problem in the 2+1D XY model at nonzero chemical potential.

Findings

Sign problem severity is exponentially reduced in chemical potential squared.

Sign problem severity is exponentially reduced in spatial volume.

A new reweighting-based optimization approach reduces computational costs.

Abstract

We study the 2+1 dimensional XY model at nonzero chemical potential $\mu$ on deformed integration manifolds, with the aim of alleviating its sign problem. We investigate several proposals for the deformations, and considerably improve on the severity of the sign problem with respect to standard reweighting approaches. We present numerical evidence that the reduction of the sign problem is exponential both in $\mu^2$ and in the spatial volume. We also present a new approach to the optimization procedure based on reweighting, that sensibly reduces its computational cost.