Minimal residual entropy in (0+1) -dimensional non-Fermi liquids

In the large N limit a physical system might acquire a residual entropy at zero temperature even without ground-state degeneracy. At the same time poles in the two-point function might coalesce and form a branch cut. Both phenomena are related to a high density of states in the large N limit. In this paper we address the following question: Does a branch cut in the two-point function always lead to nonzero residual entropy We argue that for generic fermionic systems in 0+1 dimensions in the mean-field approximation the answer is positive: Branch cut 1/τ2Δ in the two-point function does lead to a lower bound Nlog2(1/2-Δ) for the entropy. We also comment on higher-dimensional generalizations and relations to the holographic correspondence.