The Slab Method to Measure the Topological Susceptibility

TL;DR

This paper introduces the slab method, a novel approach to measure topological susceptibility in lattice simulations, especially effective when configurations are limited to a single topological sector, demonstrated on sigma models and QCD.

Contribution

The paper presents the slab method, enabling the measurement of topological susceptibility from single-sector configurations, improving accuracy in simulations with topological sector trapping.

Findings

The slab method provides stable chi_t estimates across various flow times.

Numerical results confirm the method's effectiveness in sigma models and QCD.

The approach mitigates issues caused by topological sector trapping in simulations.

Abstract

In simulations of a model with topological sectors, algorithms which proceed in small update steps tend to get stuck in one sector, especially on fine lattices. This distorts the numerical results; in particular it is not straightforward to measure the topological susceptibility chi_t. We test a method to measure chi_t even if configurations from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as "slab". This enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models and for 2-flavour QCD. In the latter case, the gradient flow is applied for the smoothing of the gauge configurations, and the slab method results for chi_t are stable over a broad range of flow times.