Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
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DOI：
10.1103/physrevb.94.144201
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发表时间：
2016-10-04
影响因子：
3.7
通讯作者：
Garcia-Garcia, Antonio M.
中科院分区：
文献类型：
--
作者：
Bertrand, Corentin L.;Garcia-Garcia, Antonio M.
用能级统计方法研究了多体局域跃迁金属侧随机场中的一维XXZ自旋链。对于固定的相互作用，在多体局部化过渡下的中间无序，我们发现，随着渐近，数量方差的增长速度比线性增长快，并且指数依赖于无序。这与光谱中异常索利斯能量的存在是一致的。在非相互作用的无序金属中，这是一个与粒子在样品中扩散的典型时间有关的能量标度。在相互作用的情况下，它似乎与一个更复杂的异常扩散过程有关。这种解释与最近的说法并不完全一致，即对于中间无序，水平统计是由具有幂律衰减相互作用的等离子体模型描述的，其数量方差增长慢于线性。当无序度进一步增加时，仍然在金属侧，索利斯能量逐渐被冲掉。在我们可以探索的尺度范围内，水平统计量是尺度不变的，并且在多体局部化转换时接近泊松统计量。稍微低于多体局域化跃迁，由临界统计描述的光谱相关性在数量上类似于安德森跃迁中的高维、非相互作用、无序导体。
We study a one-dimensional XXZ spin chain in a random field on the metallic side of the many-body localization transition by level statistics. For a fixed interaction, and intermediate disorder below the many-body localization transition, we find that, asymptotically, the number variance grows faster than linear with a disorder-dependent exponent. This is consistent with the existence of an anomalous Thouless energy in the spectrum. In noninteracting disordered metals, this is an energy scale related to the typical time for a particle to diffuse across the sample. In the interacting case, it seems related to a more intricate anomalous diffusion process. This interpretation is not fully consistent with recent claims that for intermediate disorder, level statistics are described by a plasma model with power-law decaying interactions whose number variance grows slower than linear. As disorder is further increased, still on the metallic side, the Thouless energy is gradually washed out. In the range of sizes we can explore, level statistics are scale invariant and approach Poisson statistics at the many-body localization transition. Slightly below the many-body localization transition, spectral correlations, well described by critical statistics, are quantitatively similar to those of a high-dimensional, noninteracting, disordered conductor at the Anderson transition.