Selected inversion as key to a stable Langevin evolution across the QCD phase boundary

TL;DR

This paper demonstrates that using selected inversion with PARDISO enables stable complex Langevin simulations across the QCD phase boundary at nonzero chemical potential, overcoming previous breakdown issues.

Contribution

The study introduces the application of selected inversion via PARDISO to stabilize complex Langevin evolution in full QCD simulations across phase transitions.

Findings

Stable Langevin evolution across phase boundary achieved.

Selected inversion improves drift term estimation.

Simulations successfully performed in previously problematic regions.

Abstract

We present new results of full QCD at nonzero chemical potential. In PRD 92, 094516 (2015) the complex Langevin method was shown to break down when the inverse coupling decreases and enters the transition region from the deconfined to the confined phase. We found that the stochastic technique used to estimate the drift term can be very unstable for indefinite matrices. This may be avoided by using the full inverse of the Dirac operator, which is, however, too costly for four-dimensional lattices. The major breakthrough in this work was achieved by realizing that the inverse elements necessary for the drift term can be computed efficiently using the selected inversion technique provided by the parallel sparse direct solver package PARDISO. In our new study we show that no breakdown of the complex Langevin method is encountered and that simulations can be performed across the phase boundary.