On minimal residual entropy in non-Fermi liquids

TL;DR

This paper investigates whether a branch cut in the 2-point function of fermionic systems always results in residual entropy at zero temperature, establishing a connection between spectral features and entropy in large N limits.

Contribution

It demonstrates that in 0+1 dimensional fermionic systems, a branch cut in the 2-point function implies a non-zero lower bound on residual entropy, linking spectral properties to thermodynamic behavior.

Findings

Branch cut in 2-point function implies residual entropy lower bound

Residual entropy is related to the branch cut exponent and system size

Comments on higher-dimensional cases and holographic implications

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.