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

Keitro Nagata,Jun Nishimura,Shinji Shimasaki,M Della Morte,C Pena Ruano,E Gámiz Sánchez,P Fritzsch

doi:10.1051/epjconf/201817507017

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 intro-duce 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 43 × 8 lattice and show that our method works well even in the region where the reweighing 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.

Highlights

Investigating the QCD phase diagram at finite density and temperature is one of the central issues in modern theoretical physics
We look at the probability distribution of the drift term shown in figure 1 (Top-Right), where each line corresponds to each data point in figure 1 (Top-Left)
We find that the results for α = 0.2, 0.3 are not reliable because the probability distribution of the drift term falls off with a power law

Summary

Introduction

Investigating the QCD phase diagram at finite density and temperature is one of the central issues in modern theoretical physics. QCD at high density and low temperature is interesting due to its relevance to the state of dense matter that is considered to be realized in astronomical objects like neutron stars It is known, that QCD in this parameter region suffers from a severe sign problem, which makes it practically inaccessible by conventional lattice QCD simulations based on the importance sampling. The CLM is based on the stochastic time evolution for the complexified dynamical variables using the complex Langevin equation Since this method does not rely on the probabilistic interpretation of the Boltzmann weight in the path integral formulation of the original theory, one has a chance to solve the sign problem. In applying the CLM, it is extremely important to judge the reliability of the obtained results by monitoring the asymptotic behavior of the drift distribution

Methods

Results

Conclusion