arXiv subjects
Publications and source records attributed to Ruth Schulte.
We consider a multi-dimensional continuum Schr\"odinger operator $H$ which is given by a perturbation of the negative Laplacian by a compactly supported bounded potential. We show that, for a fairly large class of test functions, the second-order Szeg\H{o}-type asymptotics for the spatially truncated Fermi projection of $H$ is independent of the potential and, thus, identical to the known asymptotics of the Laplacian.
We study the free XXZ quantum spin model defined on a ring of size $L$ and show that the bipartite entanglement entropy of eigenstates belonging to the first energy band above the vacuum ground state satisfies a logarithmically corrected area law. Along the way, we show a Combes-Thomas estimate for fiber operators which can also be applied to discrete many-particle Schrödinger operators on more general translation-invariant graphs.
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.
We consider the random dimer model in one space dimension with Bernoulli disorder. For sufficiently small disorder, we show that the entanglement entropy exhibits at least a logarithmically enhanced area law if the Fermi energy coincides with a critical energy of the model where the localisation length diverges.