Enhanced area law in the Widom-Sobolev formula for the free Dirac operator in arbitrary dimension

Abstract

We prove a logarithmically enhanced area law for all Rényi entanglement entropies of the ground state of a free gas of relativistic Dirac fermions. Such asymptotics occur in any dimension if the modulus of the Fermi energy is larger than the mass of the particles and in the massless case at Fermi energy zero in one space dimension. In all other cases of mass, Fermi energy and dimension, the entanglement entropy grows no faster than the area of the involved spatial region. The result is established for a general class of test functions which includes the ones corresponding to Rényi entropies and relies on a recently proved extension of the Widom-Sobolev formula to matrix-valued symbols by the authors.

18 pages

References in corpus (5)

• On the Area Law for Disordered Free Fermions
• The Fermionic Entanglement Entropy and Area Law for the Relativistic Dirac Vacuum State
• The Widom-Sobolev formula for discontinuous matrix-valued symbols
• The Fermionic Entanglement Entropy of the Vacuum State of a Schwarzschild Black Hole Horizon
• Rényi entropies of the free Fermi gas in multi-dimensional space at high temperature

Cited by in corpus (1)

• An enhanced term in the Szegő-type asymptotics for the free massless Dirac operator