Stability of the enhanced area law of the entanglement entropy
arXiv:2004.02700 · doi:10.1007/s00023-020-00961-x
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.
arXiv commentChanges in v2: result extended from cubes to Lipschitz domains with piecewise smooth boundary
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- 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