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.
- Publication:
-
Physical Review B
- Pub Date:
- January 2016
- DOI:
- 10.1103/PhysRevB.93.041424
- arXiv:
- arXiv:1508.07293
- Bibcode:
- 2016PhRvB..93d1424S
- Keywords:
-
- Condensed Matter - Disordered Systems and Neural Networks;
- Condensed Matter - Statistical Mechanics;
- Quantum Physics
- E-Print:
- 5 pages, 3 figures