Alternating Descent Method for Gauge Cooling of Complex Langevin Simulations

TL;DR

This paper introduces a new gauge cooling solver for complex Langevin simulations in lattice QCD, improving performance over traditional methods, especially on large lattices, through a parameter-free optimization approach.

Contribution

A novel parameter-free gauge cooling solver is proposed, enhancing efficiency and scalability in complex Langevin simulations for lattice QCD.

Findings

The new solver outperforms classical gradient descent in large lattice scenarios.

Numerical tests confirm the effectiveness of the proposed algorithm.

The method simplifies the optimization process by removing parameters.

Abstract

We study the gauge cooling technique for the complex Langevin method applied to the computation in lattice quantum chromodynamics. We propose a new solver of the minimization problem that optimizes the gauge, which does not include any parameter in each iteration, and shows better performance than the classical gradient descent method especially when the lattice size is large. Two numerical tests are carried out to show the effectiveness of the new algorithm.