Numerical Study of the Chiral Separation Effect in Two-Color QCD at Finite Density

TL;DR

This study investigates the Chiral Separation Effect in two-color QCD at finite density, revealing its behavior across different phases and providing bounds on diagram contributions, with implications for understanding QCD-like theories.

Contribution

It offers the first lattice study of the CSE in SU(2) gauge theory at finite density, showing its suppression in the confinement phase and bounding disconnected diagram effects.

Findings

CSE matches free quark results at high temperatures

CSE is suppressed in the confinement regime at low temperatures

Disconnected diagrams contribute negligibly to the CSE

Abstract

We study the Chiral Separation Effect (CSE) in finite-density SU(2) lattice gauge theory with dynamical quarks. We find that the CSE is well described by the free quark result in the high-temperature quark-gluon plasma phase. As one enters the confinement regime with broken chiral symmetry at chemical potential smaller than half of the pion mass, the CSE response is gradually suppressed towards low temperatures in comparison to the free quark result. This suppression can be approximately described by assuming that the CSE current is proportional to the charge density, rather than the chemical potential, as suggested in the literature (ArXiv:1712.01256, Phys.Rev.D97(2018)085020). We also provide an upper bound on the contribution of disconnected fermionic diagrams to the CSE, which is consistent with zero within our statistical errors and small compared to that of the connected diagrams. Our results are obtained mainly in the QCD-like regime of SU(2) gauge theory at low densities, and hence should be at least qualitatively applicable to QCD as well.