Measuring the Topological Susceptibility in a Fixed Sector

TL;DR

This paper evaluates a method to measure topological susceptibility in field theories even when the topological charge is frozen, using correlation of charge density, with successful tests in various models including promising results in QCD.

Contribution

It introduces and validates a correlation-based method for measuring topological susceptibility in regimes with frozen topology, applicable to complex gauge theories.

Findings

Accurate measurements in non-linear sigma-models and 2d Abelian gauge theory.

Promising results obtained in 4d SU(2) Yang-Mills theory.

Method is feasible even with topologically frozen Markov chains.

Abstract

For field theories with a topological charge Q, it is often of interest to measure the topological susceptibility chi_t = ( < Q^2 > - < Q >^2 ) / V. If we manage to perform a Monte Carlo simulation where Q changes frequently, chi_t can be evaluated directly. However, for local update algorithms and fine lattices, the auto-correlation time with respect to Q tends to be extremely long, which invalidates the direct approach. Nevertheless, the measurement of chi_t is still feasible, even when the entire Markov chain is topologically frozen. We test a method for this purpose, based on the correlation of the topological charge density, as suggested by Aoki, Fukaya, Hashimoto and Onogi. Our studies in non-linear sigma-models and in 2d Abelian gauge theory yield accurate results for chi_t, which confirm that the method is applicable. We also obtain promising results in 4d SU(2) Yang-Mills theory, which suggest the applicability of this method in QCD.