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arXiv 1508.04436cond-mat.dis-nncond-mat.str-el
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非平衡局域化和无序与相互作用之间的相互作用

Nonequilibrium localization and the interplay between disorder and interactions

Eduardo Mascarenhas, Helena Braganca, R. Drumond, M. C. O. Aguiar, M. Franca Santos

摘要:

研究了封闭量子系统中无序与相互作用之间的非平衡相互作用。我们的分析基础上的动态状态空间本地化的概念,计算通过Loschirk回声。虽然真实空间和状态空间本地化是独立的概念,一般来说,我们表明,这两个角度可以直接连接通过一个特定的选择的初始状态,即最大本地化状态(ML状态)。我们的数值计算表明,在非相互作用的情况下,平均回波被发现是单调增加的无序;这些结果是在单粒子的情况下,回波被发现是成反比的本地化长度与分析评价一致。我们还表明,对于相互作用的系统,平衡可能发生的长度尺度是有界的,这样的界限是较小的ML-状态的平均回声越大。当混乱和相互作用,都是本地化机制,同时在发挥回声功能的非单调行为,表明一个非平凡的相互作用的两个过程。这种相互作用引起的动态,这是伴随着在实空间中的离域。这种非单调行为也存在于有效的可积性,我们通过评估间隙统计。

英文摘要:

We study the nonequilibrium interplay between disorder and interactions in a closed quantum system. We base our analysis on the notion of dynamical state-space localization, calculated via the Loschmidt echo. Although real-space and state-space localization are independent concepts in general, we show that both perspectives may be directly connected through a specific choice of initial states, namely, maximally localized states (ML-states). We show numerically that in the noninteracting case the average echo is found to be monotonically increasing with increasing disorder; these results are in agreement with an analytical evaluation in the single particle case in which the echo is found to be inversely proportional to the localization length. We also show that for interacting systems, the length scale under which equilibration may occur is upper bounded and such bound is smaller the greater the average echo of ML-states. When disorder and interactions, both being localization mechanisms, are simultaneously at play the echo features a non-monotonic behaviour indicating a non-trivial interplay of the two processes. This interplay induces delocalization of the dynamics which is accompanied by delocalization in real-space. This non-monotonic behaviour is also present in the effective integrability which we show by evaluating the gap statistics.

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