Spectral statistics across the many-body localization transition Journal Article

Author(s): Serbyn, Maksym; Moore, Joel E
Article Title: Spectral statistics across the many-body localization transition
Abstract: The many-body localization transition (MBLT) between ergodic and many-body localized phases in disordered interacting systems is a subject of much recent interest. The statistics of eigenenergies is known to be a powerful probe of crossovers between ergodic and integrable systems in simpler examples of quantum chaos. We consider the evolution of the spectral statistics across the MBLT, starting with mapping to a Brownian motion process that analytically relates the spectral properties to the statistics of matrix elements. We demonstrate that the flow from Wigner-Dyson to Poisson statistics is a two-stage process. First, a fractal enhancement of matrix elements upon approaching the MBLT from the delocalized side produces an effective power-law interaction between energy levels, and leads to a plasma model for level statistics. At the second stage, the gas of eigenvalues has local interactions and the level statistics belongs to a semi-Poisson universality class. We verify our findings numerically on the XXZ spin chain. We provide a microscopic understanding of the level statistics across the MBLT and discuss implications for the transition that are strong constraints on possible theories.
Journal Title: Physical Review B
Volume: 93
Issue 4
ISSN: 1550-235X
Publisher: American Physical Society  
Date Published: 2016-01-29
DOI: 10.1103/PhysRevB.93.041424
Open access: yes (repository)