Complex Langevin simulations with a kernel

TL;DR

This paper explores the use of kernels in complex Langevin simulations to improve convergence, introduces a new correctness criterion, and applies machine learning to optimize kernels in lattice gauge theories, with initial results in QCD.

Contribution

It presents a novel approach using kernels to address convergence issues in complex Langevin simulations and introduces a new necessary and sufficient correctness condition.

Findings

Kernels can solve wrong convergence in toy models

A new correctness criterion for complex Langevin is proposed

Preliminary machine learning results in QCD simulations

Abstract

We discuss recent developments regarding the use of kernels in complex Langevin simulations. In particular, we outline how a kernel can be used to solve the problem of wrong convergence in a simple toy model. Since conventional correctness criteria for complex Langevin results are only necessary but not sufficient, the correct convergence of complex Langevin simulations is not always straightforward to assess. Hence, we furthermore discuss a condition for correctness that we have recently derived, which is both necessary and sufficient. Finally, we outline a machine-learning approach for finding suitable kernels in lattice gauge theories and present preliminary results of its application to the heavy-dense limit of QCD.