2015/08/28 by Maksym Serbyn, Joel E. Moore · 4 citations
Mathematics · Physics and Astronomy · #Brownian motion #Eigenvalues and eigenvectors #Ergodic theory #Integrable system #Mathematical analysis #Mathematical physics #Mathematics #Opinion Dynamics and Social Influence #Physics #Quantum many-body systems #Quantum mechanics #Random matrix #Statistical physics #Statistics #Theoretical and Computational Physics #Universality (dynamical systems) #cond-mat.dis-nn #cond-mat.stat-mech #quant-ph
paper · pdf · doi:10.1103/physrevb.93.041424
published as Phys. Rev. B 93, 041424 (2016) · 5 pages, 3 figures
arxiv created 2015/08/28 · openalex publication_date 2016/01/29 · arxiv updated 2016/02/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.