On complex Langevin dynamics and zeroes of the measure I: Formal proof and simple models

TL;DR

This paper investigates how zeroes of the fermion determinant influence the complex Langevin method's theoretical foundation, analyzing pole effects and potential issues in simple models relevant to QCD.

Contribution

It provides a formal analysis of the impact of drift poles on the complex Langevin approach and explores related issues in simplified models applicable to QCD.

Findings

Poles in the drift can invalidate the formal justification of complex Langevin.

Simple models reveal potential issues caused by these poles in the simulation.

The analysis informs the applicability of complex Langevin to dense QCD simulations.

Abstract

In the complex Langevin approach to lattice simulations at nonzero density, zeroes of the fermion determinant lead to a meromorphic drift and hence a need to revisit the theoretical derivation. We discuss how poles in the drift affect the formal justification of the approach and then explore the various potential issues in simple models, in a manner that is applicable to heavy dense and full QCD.