AI 中文总结
研究半平面上朗道哈密顿量基态的纠缠熵，发现边界条件虽改变谱性质但不影响纠缠熵主导行为，已证该哈密顿量基态有严格面积律，还提出关于绝对连续谱保证对数增强面积律所需条件的问题。
AI 中文摘要
我们研究了定义在有边界区域上的哈密顿量基态的纠缠熵。令人惊讶的是，边界条件能极大改变谱及其性质，但不改变纠缠熵的主导行为。全平面上的朗道哈密顿量有纯点谱且基态呈现严格面积律，而半平面上的朗道哈密顿量有纯绝对连续谱，我们证明其基态也有严格面积律。我们提出问题：对于绝对连续谱，需要何种额外或更精细条件才能保证像拉普拉斯算子那样有对数增强的面积律。
英文摘要
We study the entanglement entropy of ground states of a Hamiltonian defined on a domain with a boundary. Surprisingly, boundary conditions can change the spectrum and the nature of the spectrum drastically but not the leading behaviour of the entanglement entropy. As is well-known, the Landau Hamiltonian on the full plane has pure point spectrum (the infinitely degenerate Landau levels) and ground states display a so-called strict area law. On the other hand, the Landau Hamiltonian on the half-plane has purely absolutely continuous spectrum and yet we prove a strict area law for its ground states. We raise the question of what extra or finer conditions on the absolutely continuous spectrum are necessary to guarantee a logarithmically enhanced area-law as we have for the Laplace operator.
CommentsThe links in the references were partially broken in the first upload, which are now fixed
