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The Interplay of Localization and Interactions in Quantum Many-Body Systems.

机译：量子多体系统中的定位和相互作用的相互作用。

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摘要

Disorder and interactions both play crucial roles in quantum transport. Decades ago, Mott showed that electron-electron interactions can lead to insulating behavior in materials that conventional band theory predicts to be conducting. Soon thereafter, Anderson demonstrated that disorder can localize a quantum particle through the wave interference phenomenon of Anderson localization. Although interactions and disorder both separately induce insulating behavior, the interplay of these two ingredients is subtle and often leads to surprising behavior at the periphery of our current understanding. Modern experiments probe these phenomena in a variety of contexts (e.g., disordered superconductors, cold atoms, photonic waveguides, etc.); thus, theoretical and numerical advancements are urgently needed. In this thesis, we report progress on understanding two contexts in which the interplay of disorder and interactions is especially important.;The first is the so-called "dirty" or random boson problem. In the past decade, a strong-disorder renormalization group (SDRG) treatment by Altman, Kafri, Polkovnikov, and Refael has raised the possibility of a new unstable fixed point governing the superfluid-insulator transition in the one-dimensional dirty boson problem. This new critical behavior may take over from the weak-disorder criticality of Giamarchi and Schulz when disorder is sufficiently strong. We analytically determine the scaling of the superfluid susceptibility at the strong-disorder fixed point and connect our analysis to recent Monte Carlo simulations by Hrahsheh and Vojta. We then shift our attention to two dimensions and use a numerical implementation of the SDRG to locate the fixed point governing the superfluid-insulator transition there. We identify several universal properties of this transition, which are fully independent of the microscopic features of the disorder.;The second focus of this thesis is the interplay of localization and interactions in systems with high energy density (i.e., far from the usual low energy limit of condensed matter physics). Recent theoretical and numerical work indicates that localization can survive in this regime, provided that interactions are sufficiently weak. Stronger interactions can destroy localization, leading to a so-called many-body localization transition. This dynamical phase transition is relevant to questions of thermalization in isolated quantum systems: it separates a many-body localized phase, in which localization prevents transport and thermalization, from a conducting ("ergodic") phase in which the usual assumptions of quantum statistical mechanics hold. Here, we present evidence that many-body localization also occurs in quasiperiodic systems that lack true disorder.
机译：无序和相互作用在量子传输中都起着至关重要的作用。数十年前，莫特（Mott）表明，电子与电子的相互作用会导致传统能带理论预测会发生导电的材料产生绝缘行为。此后不久，安德森证明无序可以通过安德森定位的波干扰现象来定位量子粒子。尽管交互作用和无序状态分别引起绝缘行为，但这两种成分的相互作用是微妙的，并经常在我们目前的理解范围内导致令人惊讶的行为。现代实验在各种情况下（例如无序的超导体，冷原子，光子波导等）探究这些现象;因此，迫切需要理论和数值上的进步。在这篇论文中，我们报告了在理解两种情况下的进展，在这种情况下，无序和相互作用的相互作用尤为重要。第一个是所谓的“肮脏”或随机玻色子问题。在过去的十年中，由Altman，Kafri，Polkovnikov和Refael进行的强异常重整化组（SDRG）处理，提出了新的不稳定定点控制一维脏玻色子问题中超流体-绝缘体转变的可能性。当疾病足够强烈时，这种新的临界行为可能会取代Giamarchi和Schulz的弱病临界。我们分析性地确定了强流不动点上的超流体敏感性的标度，并将我们的分析与Hrahsheh和Vojta的最新蒙特卡洛模拟相联系。然后，我们将注意力转移到两个维度，并使用SDRG的数值实现来定位控制超流体-绝缘体过渡的固定点。我们确定了这种转变的几个普遍特性，它们完全独立于该疾病的微观特征。本论文的第二个重点是高能量密度（即远离通常的低能量）在系统中的定位和相互作用凝聚态物理极限）。最近的理论和数值研究表明，只要相互作用足够弱，本地化就可以在这种情况下生存。较强的交互作用会破坏本地化，从而导致所谓的多体本地化过渡。此动态相变与孤立的量子系统中的热化问题有关：它将多体局部化相（其中局部化阻止了运输和热化）与传导（“遍历”）相分离，在传导相中，通常采用量子统计力学假设保持。在这里，我们提供的证据表明，多体定位也发生在缺乏真正障碍的准周期系统中。

著录项

  • 作者

    Iyer, Shankar.;

  • 作者单位

    California Institute of Technology.;

  • 授予单位 California Institute of Technology.;
  • 学科 Physics Quantum.;Physics Condensed Matter.
  • 学位 Ph.D.
  • 年度 2013
  • 页码 245 p.
  • 总页数 245
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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