Leschke, H; Sobolev, AV; Spitzer, W; (2016) Large-scale behaviour of local and entanglement entropy of the free Fermi gas at any temperature. Journal Of Physics A: Mathematical And Theoretical , 49 (30) , Article 30LT04. 10.1088/1751-8113/49/30/30LT04.

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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 $T\gt 0$. 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 $T\downarrow 0$, the leading large-scale term of the thermal EE considerably simplifies and displays a $\mathrm{ln}(1/T)$-singularity which one may identify with the known logarithmic enhancement at T = 0 of the so-called area-law scaling.

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