Metadynamics Surfing on Topology Barriers in the Schwinger Model

TL;DR

This paper investigates the use of metadynamics to address topological freezing in lattice simulations of the Schwinger model, aiming to improve sampling efficiency across topological sectors.

Contribution

It demonstrates how metadynamics can mitigate topological freezing and explores the behavior of collective variables, with potential implications for higher-dimensional theories.

Findings

Metadynamics helps overcome topological barriers in the Schwinger model.

Analysis of collective variable scaling behavior.

Discussion of potential extensions to SU(3) theory.

Abstract

Topological freezing is a well known problem in lattice simulations: with shrinking lattice spacing a transition between topological sectors becomes increasingly improbable, leading to a problematic increase of the autocorrelation time regarding several observables. We present our investigation of metadynamics as a solution for topological freezing in the Schwinger model. Specifically, we take a closer look at the collective variable and its scaling behaviour, visualize the effects of topological freezing and how metadynamics helps in that respect and explore alternatives for a more efficient building process. Possible implications for and differences to four-dimensional SU(3) theory are briefly discussed.