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 the upper bound is to use a limiting absorption principle for such kinds of Schrödinger operators.

中文翻译：

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纠缠熵的增强面积定律的稳定性

我们考虑多维连续体Schrödinger算子，该算子由负拉普拉斯算子受紧致支持势的扰动给出。我们在准准费米气体的基态的二重纠缠熵上建立了一个上界和一个下界。边界证明，与自由费米气体不受干扰的情况一样，纠缠熵的缩放行为仍保持对数增强的面积定律。上限的中心思想是对此类Schrödinger算子使用限制吸收原理。