Adaptive stepsize and instabilities in complex Langevin dynamics

TL;DR

This paper introduces adaptive stepsize algorithms for complex Langevin simulations, effectively eliminating unstable trajectories in complex field theories like the XY model and dense QCD.

Contribution

The authors develop and demonstrate adaptive stepsize methods that improve stability in complex Langevin dynamics across different models.

Findings

Unstable trajectories are eliminated with adaptive stepsize.

Adaptive algorithms improve simulation stability.

Applicable to various complex field theories.

Abstract

Stochastic quantization offers the opportunity to simulate field theories with a complex action. In some theories unstable trajectories are prevalent when a constant stepsize is employed. We construct algorithms for generating an adaptive stepsize in complex Langevin simulations and find that unstable trajectories are completely eliminated. To illustrate the generality of the approach, we apply it to the three-dimensional XY model at nonzero chemical potential and the heavy dense limit of QCD.