Real time simulations of scalar fields with kernelled complex Langevin equation

TL;DR

This paper advances real-time scalar field simulations by employing kernel optimization via machine learning to mitigate boundary term issues in complex Langevin dynamics, extending simulation capabilities beyond previous limits.

Contribution

It introduces a novel kernel optimization approach using machine learning to improve the complex Langevin method for real-time scalar field simulations.

Findings

Extended simulation time range achieved

Kernel optimization reduces boundary term issues

Method surpasses previous state-of-the-art simulations

Abstract

Real time evolution of a scalar field theory is investigated. The severe sign problem is circumvented using the Complex Langevin equation. The naive application of the method breaks down for extended real times due to the appearance of boundary terms. We use the kernel freedom of the complex Langevin equation to push the breakdown to larger real-times. We search for the optimal kernel using machine learning methods. Thus, we extend the available range for 1+1d scalar simulations beyond the state of the art simulations.