Leschke, Hajo;
Sobolev, Alexander V;
Spitzer, Wolfgang;
(2022)
Rényi Entropies of the Free Fermi Gas in Multi-Dimensional Space at High Temperature.
In: Basor, Estelle and Böttcher, Albrecht and Ehrhardt, Torsten and Tracy, Craig A, (eds.)
Toeplitz Operators and Random Matrices: In Memory of Harold Widom.
(pp. 477-508).
Birkhäuser: Cham, Switzerland.
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Abstract
We study the local and (bipartite) entanglement Rényi entropies of the free Fermi gas in multi-dimensional Euclidean space Rd in thermal equilibrium. We prove positivity of the entanglement entropies with Rényi index γ ≤ 1 for all temperatures T > 0. Furthermore, for general γ > 0 we establish the asymptotics of the entropies for large T and large scaling parameter α > 0 for two different regimes – for fixed chemical potential µ ∈ R and also for fixed particle density ρ > 0. In particular, we thereby provide the last remaining building block for a complete proof of our low- and high-temperature results presented (for γ = 1) in J. Phys. A: Math. Theor. 49, 30LT04 (2016); Corrigendum. 50, 129501 (2017), but being supported there only by the basic proof ideas.
| Type: | Book chapter |
|---|---|
| Title: | Rényi Entropies of the Free Fermi Gas in Multi-Dimensional Space at High Temperature |
| ISBN-13: | 978-3-031-13850-8 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/978-3-031-13851-5_21 |
| Publisher version: | https://doi.org/10.1007/978-3-031-13851-5_21 |
| Language: | English |
| Additional information: | This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions. |
| Keywords: | Non-smooth functions of Wiener–Hopf operators; Asymptotic trace formulas; Rényi (entanglement) entropy of fermionic equilibrium states |
| UCL classification: | 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 UCL > Provost and Vice Provost Offices > UCL BEAMS UCL |
| URI: | https://discovery-pp.ucl.ac.uk/id/eprint/10150760 |
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