A microscopically motivated renormalization scheme for the MBL/ETH transition
A microscopically motivated renormalization scheme for the MBL/ETH transition
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MBL/ETH 过渡的微观驱动重整化方案
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
W. Roeck
中科院分区：
文献类型：
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作者：
Thimothée Thiery;M. Muller;W. Roeck
我们引入了一个多尺度对角化方案来研究无序量子链中多体定域相和遍历相之间的跃迁。该计划假设一个尖锐的二分法子系统，表现为本地化和谐振点，遵守本征态热化假说（ETH）。我们建立了一套定义对角化方案的微观原理，并利用它们来数值研究超大系统中的相变。在很大程度上的结果是一致的分析听话的平均场分析的计划：我们发现，在临界点的系统几乎肯定是本地化的热力学极限，托管一组热夹杂物的大小是幂律分布。在局部化侧，{em典型}局部化长度从上方有界。边界饱和后接近临界，需要一个有限的遍历包含热化一个区域的直径发散。占主导地位的热夹杂物具有分形结构，这意味着平均的衰减拉伸指数在整个本地化阶段。稍微在遍历方面热化发生通过雪崩不稳定性的几乎本地化的大部分，从而罕见的，超临界大遍历点最终热化整个样品。它们的大小在过渡处发散，而它们的密度消失。这种不稳定性的非本地，雪崩性质需要一个单一的参数标度的故障，并把离域过渡的标准临界现象的范围之外。
We introduce a multi-scale diagonalization scheme to study the transition between the many-body localized and the ergodic phase in disordered quantum chains. The scheme assumes a sharp dichotomy between subsystems that behave as localized and resonant spots that obey the Eigenstate Thermalization Hypothesis (ETH). We establish a set of microscopic principles defining the diagonalization scheme, and use them to numerically study the transition in very large systems. To a large extent the results are in agreement with an analytically tractable mean-field analysis of the scheme: We find that at the critical point the system is almost surely localized in the thermodynamic limit, hosting a set of thermal inclusions whose sizes are power-law distributed. On the localized side the {em typical} localization length is bounded from above. The bound saturates upon approach to criticality, entailing that a finite ergodic inclusion thermalizes a region of diverging diameter. The dominant thermal inclusions have a fractal structure, implying that averaged correlators decay as stretched exponentials throughout the localized phase. Slightly on the ergodic side thermalization occurs through an avalanche instability of the nearly localized bulk, whereby rare, supercritically large ergodic spots eventually thermalize the entire sample. Their size diverges at the transition, while their density vanishes. The non-local, avalanche-like nature of this instability entails a breakdown of single parameter scaling and puts the delocalization transition outside the realm of standard critical phenomena.