Stability of the enhanced area law of the entanglement entropy

Abstract

We consider a multi-dimensional continuum Schrödinger operator which is given by a perturbation of the negative Laplacian by a compactly supported potential. We establish both an upper and a lower bound on the bipartite entanglement entropy of the ground state of the corresponding quasi-free Fermi gas. The bounds prove that the scaling behaviour of the entanglement entropy remains a logarithmically enhanced area law as in the unperturbed case of the free Fermi gas. The central idea for the upper bound is to use a limiting absorption principle for such kinds of Schrödinger operators.

Changes in v2: result extended from cubes to Lipschitz domains with piecewise smooth boundary

References in corpus (3)

• Entanglement entropy of fermions in any dimension and the Widom conjecture
• On the Area Law for Disordered Free Fermions
• Asymptotic growth of the local ground-state entropy of the ideal Fermi gas in a constant magnetic field

Cited by in corpus (5)

• Stability of a Szegő-type asymptotics
• The Widom-Sobolev formula for discontinuous matrix-valued symbols
• Entanglement Entropy Bounds in the Higher Spin XXZ Chain
• Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimension
• An enhanced term in the Szegő-type asymptotics for the free massless Dirac operator