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Renyi entropy and the multifractal spectra of systems near the localization transition

机译：Renyi熵和局部转变附近系统的多重分形谱

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摘要

We show that the Renyi entropies of single particle, critical wave functions for disordered systems contain information about the multifractal spectrum. It is shown for moments of the Renyi entropy, S_n, where |n| < 1, it is possible to extract universal information about the multifractility of such systems. This is shown through a generic calculation and then illustrated through two example models. We find good agreement between our analytic formula and numerical simulations of the two test models. Our formalism is easily extendable to generic noninteracting fermion models. It is also suggested that recent experimental advances in measuring the multifractal spectrum might allow some moments of the Renyi entropy to be measured.
机译：我们表明，无序系统的单粒子，临界波函数的Renyi熵包含有关多重分形谱的信息。它显示了Renyi熵S_n的时刻，其中| n |。 <1，有可能提取有关此类系统多重分数的通用信息。这是通过常规计算显示的，然后通过两个示例模型进行了说明。我们在我们的解析公式与两个测试模型的数值模拟之间找到了很好的一致性。我们的形式主义很容易扩展到通用的非相互作用费米子模型。还建议在测量多重分形光谱方面的最新实验进展可能允许测量Renyi熵的某些时刻。

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  • 来源
    《Physical review》 |2012年第13期|134201.1-134201.4|共4页
  • 作者

    Xiao Chen; Benjamin Hsu; Taylor L. Hughes; Eduardo Fradkin;

  • 作者单位

    Department of Physics, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801-3080, USA;

    Department of Physics, Princeton University, Princeton, New Jersey 08544, USA;

    Department of Physics, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801-3080, USA;

    Department of Physics, University of Illinois at Urbana-Champaign, Champaign, Illinois 61801-3080, USA;

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  • 正文语种 eng
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  • 关键词

    weak or anderson localization; localization effects (anderson or weak localization);

    机译：弱或安德森本地化;本地化影响（安德森或弱本地化）;

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