Improved topological sampling for lattice gauge theories

TL;DR

This paper introduces a modified Hamiltonian Monte Carlo algorithm designed to improve sampling of topological sectors in lattice gauge theories, addressing critical slowing down near the continuum limit.

Contribution

A novel HMC-based sampling method that facilitates topological sector jumps, tested on 2D models and discussed in 4D SU(2) gauge theories.

Findings

Enhanced sampling of topological sectors in 2D Schwinger model.

Comparison shows improved performance over existing methods.

Discussion of challenges in 4D SU(2) gauge models.

Abstract

Standard sampling algorithms for lattice QCD suffer from topology freezing (or critical slowing down) when approaching the continuum limit, thus leading to poor sampling of the distinct topological sectors. I will present a modified Hamiltonian Monte Carlo (HMC) algorithm that triggers topological sector jumps during the assembly of Markov chain of lattice configurations. We study its performance in the 2D Schwinger model and compare it to alternative methods, such as fixing topology or master field. We then briefly discuss the difficulties of the algorithm in a SU(2) gauge model in 4D.