  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.
