Testing trivializing maps in the Hybrid Monte Carlo algorithm

TL;DR

This paper evaluates the effectiveness of approximate trivializing maps in Hybrid Monte Carlo simulations of the CP^{N-1} model, finding minimal speedup due to computational overhead and no change in continuum scaling.

Contribution

It provides an empirical assessment of using approximate trivializing maps in HMC, highlighting their limited benefits in this context.

Findings

Small improvement with leading order transformation

Additional computational overhead offsets gains

No change in scaling towards the continuum

Abstract

We test a recent proposal to use approximate trivializing maps in a field theory to speed up Hybrid Monte Carlo simulations. Simulating the CP^{N-1} model, we find a small improvement with the leading order transformation, which is however compensated by the additional computational overhead. The scaling of the algorithm towards the continuum is not changed. In particular, the effect of the topological modes on the autocorrelation times is studied.