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

Nagata, Keitaro (KEK Theory Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan and Center of Medical Information Science, Kochi Medical School, Kochi University, Kohasu, Oko-cho, Nankoku-shi, Kochi 783-8505, Japan) ; Nishimura, Jun (KEK Theory Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan and Graduate University for Advanced Studies (SOKENDAI), 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan) ; Shimasaki, Shinji (KEK Theory Center, High Energy Accelerator Research Organization, 1-1 Oho, Tsukuba, Ibaraki 305-0801, Japan and Research and Education Center for Natural Sciences, Keio University, Hiyoshi 4-1-1, Yokohama, Kanagawa 223-8521, Japan)

26 December 2018

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 ${4}^{3}×8$ lattice. While a straightforward application faces 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 $3.2\le \mu /T\le 5.6$ 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.

Published in: Physical Review D 98 (2018)