Complex Langevin calculations in finite density QCD at large $\mu/T$ with the deformation technique

TL;DR

This paper applies the complex Langevin method with a deformation technique to study finite density QCD at large chemical potential, overcoming singular-drift issues and revealing the Silver Blaze phenomenon.

Contribution

It introduces a deformation technique to extend complex Langevin calculations to large /T in finite density QCD with moderate quark mass.

Findings

Successful calculation of quark number density and chiral condensate at high /T

Identification of the Silver Blaze phenomenon in the results

Comparison with phase-quenched model highlights qualitative differences

Abstract

It is well known that investigating QCD at finite density by standard Monte Carlo methods is extremely difficult due to the sign problem. Some years ago, the complex Langevin method with gauge cooling was shown to work at high temperature, i.e., in the deconfined phase. The same method was also applied to QCD in the so-called heavy dense limit in the whole temperature region. In this paper we attempt to apply this method to the large $\mu/T$ regime with moderate quark mass using four-flavor staggered fermions on a $4^3\times 8$ lattice. While a straightforward application faces with the singular-drift problem, which spoils the validity of the method, we overcome this problem by the deformation technique proposed earlier. Explicit results for the quark number density and the chiral condensate obtained in this way for $3.2\leq \mu/T\leq 5.6$ are compared with the results for the phase-quenched model obtained by the standard rational hybrid Monte Carlo calculation. This reveals a clear difference, which is qualitatively consistent with the Silver Blaze phenomenon.