Criterion for many-body localization-delocalization phase transition Journal Article

Author(s): Serbyn, Maksym; Papić, Zlatko; Abanin, Dmitry A
Article Title: Criterion for many-body localization-delocalization phase transition
Abstract: We propose a new approach to probing ergodicity and its breakdown in one-dimensional quantum manybody 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 manybody localized (MBL) and ergodic phases. To characterize how strongly a local perturbation modifies the eigenstates, we introduce the parameter g(L) = (In (Vnm/δ)) which represents the disorder-averaged ratio of a typical matrix element of a local operator V to energy level spacing δ 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)=gc ~ 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.
Keywords: statistical mechanics; Quantum entanglement; Exact diagonalization; Decimation method; Delocalization transition; Energy level spacings; Entanglement entropy; Local perturbation; Quantum many-body systems; Renormalization-group predictions
Journal Title: Physical Review X
Volume: 5
Issue 4
ISSN: 2160-3308
Publisher: American Physical Society  
Date Published: 2015-01-01
DOI: 10.1103/PhysRevX.5.041047
Notes: We acknowledge helpful discussions with Sid Parameswaran, Andrew Potter, Antonello Scardicchio, Romain Vasseur, and especially with Ehud Altman and David Huse. We would like to thank Miles Stoudenmire for the assistance with ITensor library. Research at Perimeter Institute is supported by the Government of Canada through Industry Canada and by the Province of Ontario through the Ministry of Economic Development & Innovation. This research was supported by Gordon and Betty Moore Foundation EPiQS Initiative through Grant No. GBMF4307 (M. S.), Sloan Foundation, NSERC, and Early Researcher Award of Ontario (D. A.). This work made use of the facilities of N8 HPC Centre of Excellence, provided and funded by the N8 consortium and EPSRC (Grant No. EP/K000225/1). The Centre is coordinated by the Universities of Leeds and Manchester.
Open access: yes (repository)