Large-scale behaviour of local and entanglement entropy of the free Fermi gas at any temperature

Abstract

The leading asymptotic large-scale behaviour of the spatially bipartite entanglement entropy (EE) of the free Fermi gas infinitely extended in multidimensional Euclidean space at zero absolute temperature, T=0, is by now well understood. Here, we present and discuss the first rigorous results for the corresponding EE of thermal equilibrium states at T>0. The leading large-scale term of this thermal EE turns out to be twice the first-order finite-size correction to the infinite-volume thermal entropy (density). Not surprisingly, this correction is just the thermal entropy on the interface of the bipartition. However, it is given by a rather complicated integral derived from a semiclassical trace formula for a certain operator on the underlying one-particle Hilbert space. But in the zero-temperature limit the leading large-scale term of the thermal EE considerably simplifies and displays a ln(1/T)-singularity which one may identify with the known logarithmic enhancement at T=0 of the so-called area-law scaling.

The paper has been slightly rewritten to improve its readability. In particular, we now restrict ourselves to von Neumann entropies. The title and the abstract have been changed. The references have been updated. 10 pages

References in corpus (5)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Finite temperature entanglement negativity in conformal field theory
• Entropy and Entanglement in Quantum Ground States
• On the Area Law for Disordered Free Fermions
• Scaling of von Neumann entropy at the Anderson transition

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