无序相互作用一维系统中纠缠哈密顿量、局域化长度和稀有区的低本征值
On low eigevalues of the entanglement Hamiltonian, localization length, and rare regions in disordered interacting one-dimensional systems
摘要：
研究了无序相互作用一维多粒子系统纠缠哈密顿量的低本征值的性质及其与局域化长度的关系。第一纠缠哈密顿能级间距的平均值与基态局域化长度成正比，并且与局域化长度一样，对无序度和相互作用强度也表现出同样的依赖性。这是由于纠缠仅限于局域化长度量级的距离。第一纠缠能级间距的分布表现出高斯型行为，正如预期的能级间距远大于无序加宽。对于弱无序系统（局域长度大于样品长度），分布在低能级间距处显示出额外的峰。这是因为在某些样品中存在罕见的区域，这些区域表现出类似金属的大纠缠和大粒子数波动行为。这些中间的“微乳液”嵌入在绝缘相的金属区域进行了讨论。
英文摘要：
The properties of the low-lying eigenvalues of the entanglement Hamiltonian and their relation to the localization length of disordered interacting one-dimensional many-particle system is studied. The average of the first entanglement Hamiltonian level spacing is proportional to the ground state localization length and shows the same dependence on the disorder and interaction strength as the localization length. This is the result of the fact that entanglement is limited to distances of order of the localization length. The distribution of the first entanglement level spacing shows a Gaussian-like behavior as expected for level spacings much larger than the disorder broadening. For weakly disordered systems (localization length larger than sample length), the distribution shows an additional peak at low level spacings. This stems from rare regions in some samples which exhibit metallic-like behavior of large entanglement and large particle number fluctuations. These intermediate 'microemulsion' metallic regions embedded in the insulating phase are discussed.
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