纠缠熵的面积增强定律的稳定性
Stability of the enhanced area law of the entanglement entropy
摘要：
我们考虑一个多维连续薛定谔算子，它是由一个紧支撑势对负拉普拉斯算子的扰动给出的。我们建立了相应的准自由费米气体的基态的两体纠缠熵的上、下界。边界证明，纠缠熵的标度行为仍然是一个热力学增强面积定律，在自由费米气体的未扰动的情况下。上限的中心思想是对这类薛定谔算子使用极限吸收原理。
英文摘要：
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.
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