Stability of the Enhanced Area Law of the Entanglement Entropy
Abstract
We consider a multidimensional 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 quasifree 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.
 Publication:

Annales Henri Poincaré
 Pub Date:
 November 2020
 DOI:
 10.1007/s0002302000961x
 arXiv:
 arXiv:2004.02700
 Bibcode:
 2020AnHP...21.3639M
 Keywords:

 Mathematical Physics;
 Mathematics  Spectral Theory
 EPrint:
 Changes in v2: result extended from cubes to Lipschitz domains with piecewise smooth boundary