Numerical study of many-body localization and the associated quantum phase transitions employing the finite-temperature density-matrix-renormalization group

利用有限温度密度矩阵重正化群对多体局域化和相关量子相变进行数值研究

• 批准号: 285706534
• 负责人: Professor Dr. Ferdinand Evers
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/285706534?language=en
• 关键词: Numerical; study; many; body; localization

Due to the phenomenon of Anderson-localization there cannot be a metallic wire at zero temperature; strictly speaking, all (generic one-dimensional) wires are insulators, and the associated conductance vanishes. The effect is due to an interplay of disorder and quantum-interference that ultimately localizes all propagating modes even if the disorder strength is very weak. Until recently there was a widely held belief that the wire would turn metallic at any finite temperature due to the effect of interactions. However, about a decade ago two teams presented theoretical arguments indicating that a generalized version of Anderson localization persists in Fock-space, that inhibits delocalization unless the temperature exceeds a critical value Tc. The results of subsequent work, computational and analytical, have lent full support to these claims. The existence of many-body-localization (MBL) is nowadays considered to be confirmed; experimental tests of (MBL) have been proposed and first measurements are being discussed. MBL implies the existence of classes of many-body states that represent insulators and other classes that represent metals. Each one of these classes fills a spectral window that is separated from a neighboring window by a quantum phase transition. The goal of the present proposal is to advance our knowledge and understanding of these transitions and the neighboring phases. Specifically, we propose a computational transport study of a disordered quantum wire of spin-half and spin-less fermions with short-range interactions. Main observables will be the charge, spin and energy densities and their relaxation behavior, together with the associated dynamical conductances. Our computational tool will be the density-matrix-renormalization group (DMRG) in a finite-temperature implementation. The first part of our study focuses on the relaxation dynamics of wavepackets near the phase transition. The goal is to extract from the time-dependent moments of the wave-packet distribution the relaxation time scales near and at the quantum phase transitions. When approaching the critical temperature from above, these time scales should exhibit a singular behavior (presumably with critical exponents) that we would like to study. At present, very little is known about the critical dynamics and its temperature dependency. The topic is important not only for fundamental reasons, but also because it will likely be relevant for the analysis of future experiments. Another part of the research addresses critical exponents that describe the frequency dependency of the conductance near and at the critical point. We begin by confirming very recent results about the charge-conductivity exponents. We proceed by calculating spin- and heat-exponents, which are still unknown. A comparison of exponents will provide information about the microscopic mechanism of spin- and heat flows, such as enthalpy and entropy per particle.

由于安德森定域化现象，不可能存在零温度的金属线;严格地说，所有（一般的一维）线都是绝缘体，并且相关的电导消失。这种效应是由于无序和量子干涉的相互作用，即使无序强度很弱，量子干涉最终也会使所有传播模式局部化。 直到最近，人们还普遍认为，由于相互作用的影响，金属丝在任何有限的温度下都会变成金属。然而，大约十年前，两个团队提出了理论论据，表明在福克空间中存在广义版本的安德森局域化，除非温度超过临界值Tc，否则会抑制离域。随后的计算和分析工作的结果充分支持了这些主张。多体定域（MBL）的存在现在被认为是确认;（MBL）的实验测试已经提出，第一次测量正在讨论中。 MBL意味着存在代表绝缘体的多体态类和代表金属的其他类。这些类别中的每一个都填充了一个光谱窗口，该窗口通过量子相变与相邻窗口分开。本提案的目标是促进我们对这些过渡和相邻阶段的认识和理解。具体来说，我们提出了一个计算输运研究的无序量子线自旋半和自旋少的费米子与短程相互作用。主要的观测量将是电荷，自旋和能量密度及其弛豫行为，以及相关的动态电导。我们的计算工具将是密度矩阵重整化群（DMRG）在有限温度的实现。 我们的研究的第一部分集中在相变附近的波包的弛豫动力学。我们的目标是从波包分布的含时矩中提取量子相变附近和相变处的弛豫时间尺度。当从上面接近临界温度时，这些时间尺度应该表现出我们想要研究的奇异行为（可能具有临界指数）。 目前，人们对临界动力学及其温度依赖性知之甚少。这一主题之所以重要，不仅是因为其根本原因，而且还因为它可能与未来实验的分析相关。 另一部分的研究地址的临界指数，描述的频率依赖性的电导附近和在临界点。我们开始确认最近的结果有关的电荷电导率指数。我们继续计算自旋和热指数，这仍然是未知的。 指数的比较将提供关于自旋和热流的微观机制的信息，例如每个粒子的焓和熵。