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.
Type: | Article |
---|---|
Title: | Large-scale behaviour of local and entanglement entropy of the free Fermi gas at any temperature |
Open access status: | An open access version is available from UCL Discovery |
DOI: | 10.1088/1751-8113/49/30/30LT04 |
Publisher version: | http://dx.doi.org/10.1088/1751-8113/49/30/30LT04 |
Language: | English |
Additional information: | © 2016 IOP Publishing Ltd |
Keywords: | Science & Technology, Physical Sciences, Physics, Multidisciplinary, Physics, Mathematical, Physics, entanglement entropy, local entropy, free Fermi gas in equilibrium, semiclassical trace formulas, Wiener-hopf Operators. |
UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
URI: | https://discovery.ucl.ac.uk/id/eprint/1516617 |
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