Thermal Simulations, Open Boundary Conditions and Switches

Yannis Burnier,Lukas Mazur,Olaf Kaczmarek,Adrien Florio

doi:10.1051/epjconf/201817507004

Yannis Burnier, Lukas Mazur + Show 2 more

Open Access

https://doi.org/10.1051/epjconf/201817507004

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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 Lüscher 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.

Highlights

S U(N) gauge theories on compact and orientable manifolds admit a set of distinct vacua, labeled by an integer topological charge Q [1]
As expected, the topological charge is not quantized and the topological freezing disappears
In the right hand-side part of figure 1, we show the ratio of the topological charge variance by the lattice volumes, both for PBC and open boundary conditions (OBC) configurations

Summary

Introduction

S U(N) gauge theories on compact and orientable manifolds admit a set of distinct vacua, labeled by an integer topological charge Q [1]. The use of open boundary conditions (OBC) in the time extent has been proposed in [7] In this context, the base manifold of the simulations is not compact anymore, Q is not quantized and the topological freezing disappears. It is needed for a precise determination of transport coefficients, whose correlators are known to be sensitive to the topological sampling [14]. Atop of the topological charge not being anymore a topological invariant, OBC configurations are plagued by strong finite-size effects. We conclude by discussing outlooks on how this method could be improved

Topological Freezing and Spatial OBC

Switching the Boundaries

Conclusion