Thermal Simulations, Open Boundary Conditions and Switches

TL;DR

This paper explores using open boundary conditions in space for thermal lattice gauge theory simulations to mitigate topological charge freezing, enabling better sampling of topological sectors at non-zero temperature.

Contribution

It introduces a novel approach of applying open boundary conditions in space for thermal simulations, addressing topological freezing without disrupting periodic time boundary conditions.

Findings

Open boundary conditions lift topological barriers at finite temperature.

Strong finite-size effects are observed due to boundary conditions.

Preliminary results suggest potential for reshuffling configurations to generate non-zero topological charge.

Abstract

$SU(N)$ gauge theories on compact spaces have a non-trivial vacuum structure characterized by a countable set of topological sectors and their topological charge. In lattice simulations, every topological sector needs to be explored a number of times which reflects its weight in the path integral. Current lattice simulations are impeded by the so-called freezing of the topological charge problem. As the continuum is approached, energy barriers between topological sectors become well defined and the simulations get trapped in a given sector. A possible way out was introduced by L\"uscher and Schaefer using open boundary condition in the time extent. However, this solution cannot be used for thermal simulations, where the time direction is required to be periodic. In this proceedings, we present results obtained using open boundary conditions in space, at non-zero temperature. With these conditions, the topological charge is not quantized and the topological barriers are lifted. A downside of this method are the strong finite-size effects introduced by the boundary conditions. We also present some exploratory results which show how these conditions could be used on an algorithmic level to reshuffle the system and generate periodic configurations with non-zero topological charge.