Complex Langevin calculations in QCD at finite density

TL;DR

This paper demonstrates that the complex Langevin method can successfully perform calculations in finite-density QCD where traditional methods fail, revealing insights into quark behavior and the Fermi sphere formation.

Contribution

The study applies the complex Langevin method to finite-density QCD, showing its effectiveness and providing initial evidence of Fermi sphere formation in this regime.

Findings

Complex Langevin method enables calculations where traditional methods cannot.

Observation of a plateau in quark number expectation value consistent with Fermi distribution.

Results suggest the formation of a Fermi sphere, relevant to color superconductivity.

Abstract

We demonstrate that the complex Langevin method (CLM) enables calculations in QCD at finite density in a parameter regime in which conventional methods, such as the density of states method and the Taylor expansion method, are not applicable due to the severe sign problem. Here we use the plaquette gauge action with $\beta = 5.7$ and four-flavor staggered fermions with degenerate quark mass $m a = 0.01$ and nonzero quark chemical potential $\mu$. We confirm that a sufficient condition for correct convergence is satisfied for $\mu /T = 5.2 - 7.2$ on a $8^3 \times 16$ lattice and $\mu /T = 1.6 - 9.6$ on a $16^3 \times 32$ lattice. In particular, the expectation value of the quark number is found to have a plateau with respect to $\mu$ with the height of 24 for both lattices. This plateau can be understood from the Fermi distribution of quarks, and its height coincides with the degrees of freedom of a single quark with zero momentum, which is 3 (color) $\times$ 4 (flavor) $\times$ 2 (spin) $=24$. Our results may be viewed as the first step towards the formation of the Fermi sphere, which plays a crucial role in color superconductivity conjectured from effective theories.