Universal crossovers between entanglement entropy and thermal entropy

TL;DR

The paper proposes a universal crossover between entanglement entropy and thermal entropy in gapless quantum systems, formalizing this with a scaling ansatz $S_R(L,T)=T^{\phi} f_R(LT)$ that reproduces the correct zero- and finite-temperature limits and predicts that boundary-law violations are at most logarithmic in natural local systems. It substantiates the framework via conformal field theories, holographic calculations, and non-relativistic (Lifshitz) examples, and extends the analysis to codimension-$q$ gapless manifolds (e.g., Fermi surfaces), yielding universal terms that scale as $(k_F L)^{d-q}$ with either a constant or a logarithmic prefactor depending on parity. The work also treats fluctuations of conserved quantities and discusses potential violations, while outlining extensions to Renyi entropy, multiple regions, and deconfined critical points, thereby providing a unified picture of how low-energy degrees of freedom govern both entanglement and thermodynamics in gapless systems.

Abstract

We postulate the existence of universal crossover functions connecting the universal parts of the entanglement entropy to the low temperature thermal entropy in gapless quantum many-body systems. These scaling functions encode the intuition that the same low energy degrees of freedom which control low temperature thermal physics are also responsible for the long range entanglement in the quantum ground state. We demonstrate the correctness of the proposed scaling form and determine the scaling function for certain classes of gapless systems whose low energy physics is described by a conformal field theory. We also use our crossover formalism to argue that local systems which are "natural" can violate the boundary law at most logarithmically. In particular, we show that several non-Fermi liquid phases of matter have entanglement entropy that is at most of order $L^{d-1}\log{(L)} $ for a region of linear size $L$ thereby confirming various earlier suggestions in the literature. We also briefly apply our crossover formalism to the study of fluctuations in conserved quantities and discuss some subtleties that occur in systems that spontaneously break a continuous symmetry.