On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density

TL;DR

This study assesses the complex Langevin method's validity in simulating finite-density QCD near the deconfinement transition, finding it effective up to a certain chemical potential but failing near the phase boundary due to singular drift issues.

Contribution

It extends previous work by testing the complex Langevin method on larger lattices near the deconfinement transition, analyzing its validity and limitations in this regime.

Findings

CL method works up to bc/T=4.8 in the deconfined phase

Failure occurs near the phase boundary due to singular drift problems

Validity depends on the lattice size and proximity to the phase transition

Abstract

In our previous paper [JHEP 10 (2020) 144], we found that the complex Langevin (CL) method works for QCD at finite density on the $16^3 \times 32$ lattice in the low-temperature high-density regime within the range $\mu / T = 1.6 - 9.6$ with $\mu$ and $T$ being the quark chemical potential and the temperature, which enabled us to see a clear trend towards the formation of the Fermi sphere. Here we investigate the validity of the CL method on the $24^3 \times 12$ lattice in the deconfined phase near the deconfinement phase transition. As before, we use four-flavor staggered fermions and judge the validity using the criterion based on the probability distribution of the drift term. The spatial extent is $L = (1.3 - 2.7 {\rm ~fm} )> \Lambda_{\rm LQCD}^{-1} \sim 1{\rm ~fm}$, in contrast to our previous study with $L < \Lambda_{\rm LQCD}^{-1}$. We find that the CL method works in a broad region up to $\mu / T = 4.8$, while it starts to fail as we approach the phase boundary due to the singular drift problem, which can be understood qualitatively by extending the Banks-Casher relation to the case at finite density.