横纵混合场量子随机反铁磁Ising链能谱的大尺度行为
Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields
摘要：
近年来，很明显，表现出多体局域化（MBL）行为的系统的金属区域显示出与单粒子Anderson区域的香草金属区域完全不同的性质。在这里，我们表明，具有MBL的正则微观模型的大尺度能谱，显示在中间尺度的非普适行为，这是从单粒子安德森制度中看到的普遍性的偏差不同。揭示这种行为的关键步骤是使用奇异值分解（SVD）进行的光谱的全局展开，该分解考虑了光谱的样本波动。谱的性质可以通过scree图直接在奇异值幅值中观察到，或者通过使用SVD展开谱，然后执行多个状态的方差计算。这两种方法都揭示了一个中间规模的能量，遵循超Poisson统计。
英文摘要：
In recent years it became clear that the metallic regime of systems that exhibit a many body localization (MBL) behavior show properties which are quite different than the vanilla metallic region of the single particle Anderson regime. Here we show that the large scale energy spectrum of a canonical microscopical model featuring MBL, displays a non-universal behavior at intermediate scales, which is distinct from the deviation from universality seen in the single particle Anderson regime. The crucial step in revealing this behavior is a global unfolding of the spectrum performed using the singular value decomposition (SVD) which takes into account the sample to sample fluctuations of the spectra. The spectrum properties may be observed directly in the singular value amplitudes via the scree plot, or by using the SVD to unfold the spectra and then perform a number of states variance calculation. Both methods reveal an intermediate scale of energies which follow super Posissonian statistics.
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