Criterion for Many-Body Localization-Delocalization Phase Transition

被引:239
作者
Serbyn, Maksym [1 ]
Papic, Z. [2 ]
Abanin, Dmitry A. [3 ,4 ]
机构
[1] Univ Calif Berkeley, Dept Phys, Berkeley, CA 94720 USA
[2] Univ Leeds, Sch Phys & Astron, Leeds LS2 9JT, W Yorkshire, England
[3] Univ Geneva, Dept Theoret Phys, CH-1211 Geneva, Switzerland
[4] Perimeter Inst Theoret Phys, Waterloo, ON N2L 2Y5, Canada
来源
PHYSICAL REVIEW X | 2015年 / 5卷 / 04期
基金
加拿大自然科学与工程研究理事会; 英国工程与自然科学研究理事会;
关键词
QUANTUM-SYSTEMS; THERMALIZATION; DIFFUSION; DISORDER; ABSENCE;
D O I
10.1103/PhysRevX.5.041047
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
We propose a new approach to probing ergodicity and its breakdown in one-dimensional quantum many-body systems based on their response to a local perturbation. We study the distribution of matrix elements of a local operator between the system's eigenstates, finding a qualitatively different behavior in the many-body localized (MBL) and ergodic phases. To characterize how strongly a local perturbation modifies the eigenstates, we introduce the parameter G(L) = < ln(V-nm/delta)> , which represents the disorder-averaged ratio of a typical matrix element of a local operator V to energy level spacing delta; this parameter is reminiscent of the Thouless conductance in the single-particle localization. We show that the parameter G(L) decreases with system size L in the MBL phase and grows in the ergodic phase. We surmise that the delocalization transition occurs when G(L) is independent of system size, G(L) = G(c) similar to 1. We illustrate our approach by studying the many-body localization transition and resolving the many-body mobility edge in a disordered one-dimensional XXZ spin-1/2 chain using exact diagonalization and time-evolving block-decimation methods. Our criterion for the MBL transition gives insights into microscopic details of transition. Its direct physical consequences, in particular, logarithmically slow transport at the transition and extensive entanglement entropy of the eigenstates, are consistent with recent renormalization-group predictions.
引用
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页数:10
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