R\'enyi entropies of the free Fermi gas in multi-dimensional space at high temperature
pp. 477-508 in: "Toeplitz Operators and Random Matrices - In Memory of Harold Widom"; Editors: E. Basor, A. B\"ottcher, T. Erhardt, C. A. Tracy; Operator Theory: Advances and Applications vol. 289, Birkh\"auser/Springer Nature, Cham, 2022 We study the local and (bipartite) entang...
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Main Authors | , , |
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Format | Journal Article |
Language | English |
Published |
26.01.2022
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Online Access | Get full text |
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Summary: | pp. 477-508 in: "Toeplitz Operators and Random Matrices - In
Memory of Harold Widom"; Editors: E. Basor, A. B\"ottcher, T. Erhardt, C. A.
Tracy; Operator Theory: Advances and Applications vol. 289,
Birkh\"auser/Springer Nature, Cham, 2022 We study the local and (bipartite) entanglement R\'enyi entropies of the free
Fermi gas in multi-dimensional Euclidean space $\mathbb{R}^d$ in thermal
equilibrium. We prove positivity of the entanglement entropies with R\'enyi
index $\gamma\leq1$ for all temperatures $T>0$. Furthermore, for general
$\gamma>0$ we establish the asymptotics of the entropies for large $T$ and
large scaling parameter $\alpha>0$ for two different regimes $-$ for fixed
chemical potential $\mu\in\mathbb{R}$ and also for fixed particle density
$\rho>0$. In particular, we thereby provide the last remaining building block
for a complete proof of our low- and high-temperature results presented (for
$\gamma=1$) in J. Phys. A: Math. Theor. $\textbf{49}$, 30LT04 (2016)
[Corrigendum: $\textbf{50}$, 129501 (2017)], but being supported there only by
the basic proof ideas. |
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DOI: | 10.48550/arxiv.2201.11087 |