Testing imaginary vs. real chemical potential in finite-temperature QCD

TL;DR

This paper evaluates the feasibility of using imaginary chemical potential in lattice QCD simulations to infer properties at real chemical potential, focusing on spatial correlation lengths in the quark-gluon plasma.

Contribution

It demonstrates that analytic continuation from imaginary to real chemical potential is feasible within a limited range, providing a practical approach for finite-temperature QCD studies.

Findings

Imaginary chemical potential induces a phase transition at |mu/T| ≈ pi/3.

Observables are analytic only within a limited range of imaginary chemical potential.

Relevant information for real chemical potential can be obtained within this analytic range.

Abstract

One suggestion for determining the properties of QCD at finite temperatures and densities is to carry out lattice simulations with an imaginary chemical potential whereby no sign problem arises, and to convert the results to real physical observables only afterwards. We test the practical feasibility of such an approach for a particular class of physical observables, spatial correlation lengths in the quark-gluon plasma phase. Simulations with imaginary chemical potential followed by analytic continuation are compared with simulations with real chemical potential, which are possible by using a dimensionally reduced effective action for hot QCD. We find that for imaginary chemical potential the system undergoes a phase transition at |mu/T| \approx pi/3, and thus observables are analytic only in a limited range. However, utilising this range, relevant information can be obtained for the real chemical potential case.