Exponential reduction of the sign problem at finite density in the 2+1D XY model via contour deformations
Matteo Giordano, Kornél Kapás, S. D. Katz, Attila Pásztor, Zoltán Tulipánt
Abstract
We study the 2+1-dimensional XY model at nonzero chemical potential $\ensuremath{\mu}$ 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 ${\ensuremath{\mu}}^{2}$ and in the spatial volume. We also present a new approach to the optimization procedure based on reweighting that sensibly reduces its computational cost.
Topics & Concepts
Sign (mathematics)Reduction (mathematics)Exponential functionPhysicsApplied mathematicsMathematicsMathematical analysisGeometryQuantum Chromodynamics and Particle InteractionsTheoretical and Computational PhysicsMarkov Chains and Monte Carlo Methods