Topological Susceptibility from Slabs

TL;DR

This paper introduces a method to measure topological susceptibility in quantum field theories using slab sub-volume data, overcoming challenges posed by local update algorithms at fine lattice spacings.

Contribution

It proposes a novel approach to determine topological susceptibility from a single topological sector using Gaussian assumptions on slab charges, validated with numerical results.

Findings

Method successfully measures chi_t from one sector data.

Numerical validation in non-linear sigma-models confirms effectiveness.

Overcomes limitations of traditional Monte Carlo methods at fine lattice spacings.

Abstract

In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility chi_t. In principle it seems straightforward to measure chi_t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure chi_t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models.