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首页> 外文期刊>Physical review >Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems
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Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems

机译：QuaSiodic Systems中定位转换时单参数和单参数缩放的传输，多重性和崩溃

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There has been a revival of interest in localization phenomena in quasiperiodic systems with a view to examining how they differ fundamentally from such phenomena in random systems. Motivated by this, we study transport in the quasiperiodic, one-dimensional Aubry-Andre model and its generalizations to two and three dimensions. We study the conductance of open systems, connected to leads, as well as the Thouless conductance, which measures the response of a closed system to boundary perturbations. We find that these conductances show signatures of a metal-insulator transition from an insulator, with localized states, to a metal, with extended states having (a) ballistic transport (one dimension), (b) superdiffusive transport (two dimensions), or (c) diffusive transport (three dimensions); precisely at the transition, the system displays subdiffusive critical states. We calculate the beta function beta(g) = d ln(g)/d ln(L) and show that, in one and two dimensions, single-parameter scaling is unable to describe the transition. Furthermore, the conductances show strong nonmonotonic variations with L and an intricate structure of resonant peaks and subpeaks. In one dimension the positions of these peaks can be related precisely to the properties of the number that characterizes the quasiperiodicity of the potential; and the L dependence of the Thouless conductance is multifractal. We find that, as dimension increases, this nonmonotonic dependence of g on L decreases and, in three dimensions, our results for beta(g) are reasonably well approximated by single-parameter scaling.
机译：拟普利周期系统中的局部化现象兴趣复兴，以期检查它们在随机系统中的这种现象根本上的不同之处。由此激励，我们研究了QuaSiperiodic，一维Aubry-Andre模型的运输及其到两个和三维的概括。我们研究开放系统的电导，连接到引线，以及无能的电导，从而测量封闭系统对边界扰动的响应。我们发现这些电导显示了从绝缘体的金属绝缘体过渡的签名，其中局部状态与局部状态到金属，其中具有（a）弹道传输（一个尺寸），（b）超级运输（两个维度）或（c）扩散运输（三维）;精确地在过渡时，系统显示潜在的关键状态。我们计算Beta函数beta（g）= d ln（g）/ d ln（l）并显示，在一个和两个维度中，单参数缩放无法描述转换。此外，电导显示出强大的非单调变化与L和谐振峰和子点套的复杂结构。在一个维度中，这些峰的位置可以精确地相关，以表征潜在的QuaSipIodicity的数量;而无数电导的L依赖性是多法的。我们发现，随着尺寸的增加，G对L对L的这种非单调依赖性降低，并且在三个方面，我们的β（g）的结果通过单参数缩放相当好地近似。

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  • 来源
    《Physical review》 |2019年第22期|224204.1-224204.10|共10页
  • 作者

    Sutradhar Jagannath; Mukerjee Subroto; Pandit Rahul; Banerjee Sumilan;

  • 作者单位

    Indian Inst Sci Ctr Condensed Matter Theory Dept Phys Bangalore 560012 Karnataka India;

    Indian Inst Sci Ctr Condensed Matter Theory Dept Phys Bangalore 560012 Karnataka India;

    Indian Inst Sci Ctr Condensed Matter Theory Dept Phys Bangalore 560012 Karnataka India;

    Indian Inst Sci Ctr Condensed Matter Theory Dept Phys Bangalore 560012 Karnataka India;

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