Complex Langevin boundary terms in lattice models

TL;DR

This paper investigates boundary terms in complex Langevin simulations, proposing a measurable formulation that helps estimate systematic errors, with results demonstrated on toy and lattice models.

Contribution

It introduces a new, cost-effective way to measure boundary terms in complex Langevin simulations, enabling direct error estimation.

Findings

Boundary terms can be systematically measured in lattice models.

The method is demonstrated on toy, 3d XY, and HDQCD models.

Results show potential for improving accuracy of complex Langevin simulations.

Abstract

In complex Langevin simulations, the insufficient decay of the probability density near infinity leads to boundary terms that spoil the formal argument for correctness. We present a formulation of this term that is cheaply measurable in lattice models, and in principle allows also the direct estimation of the systematic error of the CL method. Results for a toy model, 3d XY model and HDQCD are presented.