Computing the topological susceptibility from fixed topology QCD simulations

TL;DR

This paper investigates two methods to compute the topological susceptibility in lattice QCD when simulations are confined to a fixed topological sector, addressing challenges posed by algorithms that get stuck in a single sector.

Contribution

It introduces and compares two novel approaches for extracting topological susceptibility from fixed-topology lattice QCD data, applicable when traditional methods are hindered by algorithmic limitations.

Findings

Both methods produce consistent estimates of topological susceptibility.

Numerical results demonstrate the effectiveness of the methods in two-flavor QCD.

The approaches are viable alternatives when simulations are restricted to a single topological sector.

Abstract

The topological susceptibility is an important quantity in QCD, which can be computed using lattice methods. However, at a fine lattice spacing, or when using high quality chirally symmetric quarks, algorithms which proceed in small update steps --- in particular the HMC algorithm --- tend to get stuck in a single topological sector. In such cases, the computation of the topological susceptibility is not straightforward. Here, we explore two methods to extract the topological susceptibility from lattice QCD simulations restricted to a single topological sector. The first method is based on the correlation function of the topological charge density, while the second method relies on measuring the topological charge within spacetime subvolumes. Numerical results for two-flavor QCD obtained by using both methods are presented.