Critical slowing down of topological modes

TL;DR

This paper studies the severe critical slowing down of topological modes in lattice 2-d CP^(N-1) models, highlighting its potential universality in lattice theories with non-trivial topology like QCD.

Contribution

It demonstrates that topological modes slow down more severely than magnetic susceptibility modes, suggesting a general feature in lattice theories with topological properties.

Findings

Topological modes exhibit a critical slowing down more severe than magnetic modes.

The dynamic critical exponent for topological modes is significantly larger than 2.

Similar behavior is suggested to occur in lattice QCD and other gauge theories.

Abstract

We investigate the critical slowing down of the topological modes using local updating algorithms in lattice 2-d CP^(N-1) models. We show that the topological modes experience a critical slowing down that is much more severe than the one of the quasi-Gaussian modes relevant to the magnetic susceptibility, which is characterized by $\tau_{\rm mag} \sim \xi^z$ with $z\approx 2$. We argue that this may be a general feature of Monte Carlo simulations of lattice theories with non-trivial topological properties, such as QCD, as also suggested by recent Monte Carlo simulations of 4-d SU(N) lattice gauge theories.