On minimal residual entropy in non-Fermi liquids

Abstract

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 2-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 short note we address the question: does a branch cut in the 2-point function always lead to non-zero residual entropy? We argue that for generic fermionic systems in $0+1$ dimensions in the mean-field approximation the answer is positive: branch cut $1/{\tau }^{2\Delta }$ in the 2-point function does lead to a lower bound $N\log 2(1/2-\Delta )$ for the entropy. We also comment on higher-dimensional generalizations and relations to the holographic correspondence.

14 pages + one appendix, 3 Figures. v2: comments added