Rényi Entropies of the Free Fermi Gas in Multi-Dimensional Space at High Temperature - Leschke, Hajo; Sobolev, Alexander V.; Spitzer, Wolfgang (Springer Science and Business Media Deutschland GmbH, 2022)
We study the local and (bipartite) entanglement Rényi entropies of the free Fermi gas in multi-dimensional Euclidean space 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 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.
CRIS-Team Scopus Importer:2024-12-16
Keywords: Asymptotic trace formulas; Non-smooth functions of Wiener–Hopf operators; Rényi (entanglement) entropy of fermionic equilibrium states