Complex Langevin simulation of QCD at finite density and low temperature using the deformation technique

TL;DR

This paper applies the complex Langevin method with a deformation technique to simulate QCD at finite density and low temperature, successfully overcoming the sign problem and observing the Silver Blaze phenomenon.

Contribution

It introduces a deformation parameter in the Dirac operator combined with gauge cooling to reliably simulate QCD at finite density, extending the applicability of the complex Langevin method.

Findings

Successful simulation on a small lattice demonstrating the method's effectiveness.

Observation of the delayed onset of baryon density indicating the Silver Blaze phenomenon.

Method outperforms reweighting techniques in severe sign problem regions.

Abstract

We study QCD at finite density and low temperature by using the complex Langevin method. We employ the gauge cooling to control the unitarity norm and introduce a deformation parameter in the Dirac operator to avoid the singular-drift problem. The reliability of the obtained results are judged by the probability distribution of the magnitude of the drift term. By making extrapolations with respect to the deformation parameter using only the reliable results, we obtain results for the original system. We perform simulations on a $4^3\times 3$ lattice and show that our method works well even in the region where the reweighting method fails due to the severe sign problem. As a result we observe a delayed onset of the baryon number density as compared with the phase-quenched model, which is a clear sign of the Silver Blaze phenomenon.