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 toward 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 [Phys. Rev. D 97, 085020 (2018). 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.

• Received 14 December 2020
• Accepted 2 July 2021

DOI:https://doi.org/10.1103/PhysRevD.104.014511

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Published by the American Physical Society