Rényi entropies of the free Fermi gas in multi-dimensional space at high temperature

Abstract

We study the local and (bipartite) entanglement Rényi entropies of the free Fermi gas in multi-dimensional Euclidean space in thermal equilibrium. We prove the positivity of the entanglement entropies at any temperature for Rényi index γ ≤ 1. Furthermore, for general γ > 0 we establish the asymptotics of the entropies at high temperature and at large scaling parameter for two different regimes -for fixed chemical potential and also for fixed particle density. 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.

Entanglement entropies of an interval in the free Schrödinger field theory at finite density

“…It would be interesting to study the entanglement entropies of an interval on the line for the fermionic spinless Schrödinger model in a general Gibbs state, where both the density and the temperature occur [173][174][175]. The most important generalisation to explore is the spinfull model with a quartic interaction [40][41][42].…”