Large-scale behaviour of local and entanglement entropy of the free Fermi gas at any temperature In memory of Enrico Fermi (1901-1954) on the occasion of the 90 th birthday of the ideal Fermi gas
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...
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Published in | Journal of physics. A, Mathematical and theoretical Vol. 49; no. 30 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
IOP Publishing
16.06.2016
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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 > 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 ↓ 0 , 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. |
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AbstractList | 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 T ↓ 0 , 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. |
Author | Sobolev, Alexander V Leschke, Hajo Spitzer, Wolfgang |
Author_xml | – sequence: 1 givenname: Hajo surname: Leschke fullname: Leschke, Hajo email: hajo.leschke@physik.uni-erlangen.de organization: FernUniversität Hagen Fakultät für Mathematik und Informatik, Universitätsstraße 1, D-58097 Hagen, Germany – sequence: 2 givenname: Alexander V surname: Sobolev fullname: Sobolev, Alexander V email: a.sobolev@ucl.ac.uk organization: University College London Department of Mathematics, Gower Street, London, WC1E 6BT, UK – sequence: 3 givenname: Wolfgang surname: Spitzer fullname: Spitzer, Wolfgang email: wolfgang.spitzer@fernuni-hagen.de organization: FernUniversität Hagen Fakultät für Mathematik und Informatik, Universitätsstraße 1, D-58097 Hagen, Germany |
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SubjectTerms | entanglement entropy free Fermi gas in equilibrium local entropy semiclassical trace formulas |
Title | Large-scale behaviour of local and entanglement entropy of the free Fermi gas at any temperature In memory of Enrico Fermi (1901-1954) on the occasion of the 90 th birthday of the ideal Fermi gas |
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