Interpreting Numerical Measurements in Fixed Topological Sectors

TL;DR

This paper investigates a method to accurately approximate full topological sector results in quantum field theories by combining measurements from individual sectors, overcoming long auto-correlation issues in simulations.

Contribution

It tests and demonstrates a topological summation approach for reliable measurements across sectors in various models, including O(N), SU(2), and Schwinger models.

Findings

Energy levels and susceptibilities can be accurately estimated.

The approach works under suitable conditions.

Effective in multiple quantum field theory models.

Abstract

For quantum field theories with topological sectors, Monte Carlo simulations on fine lattices tend to be obstructed by an extremely long auto-correlation time with respect to the topological charge. Then reliable numerical measurements are feasible only within individual sectors. The challenge is to assemble such restricted measurements in a way that leads to a substantiated approximation to the fully fledged result, which would correspond to the correct sampling over the entire set of configurations. We test an approach for such a topological summation, which was suggested by Brower, Chandrasekharan, Negele and Wiese. Under suitable conditions, energy levels and susceptibilities can be obtained to a good accuracy, as we demonstrate for O(N) models, SU(2) Yang-Mills theory, and for the Schwinger model.