Stability of the Enhanced Area Law of the Entanglement Entropy

Peter Müller, Ruth Schulte
2020 Annales de l'Institute Henri Poincare. Physique theorique  
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 bound 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
more » ... central idea for the upper bound is to use a limiting absorption principle for such kinds of Schrödinger operators.
doi:10.1007/s00023-020-00961-x fatcat:hkxvdeulrbgsriho7e3k4ufnoi