Spectral statistics across the many-body localization transition

Understand

The many-body localization transition (MBLT) between ergodic and many-body localized phase in disordered interacting systems is a subject of much recent interest.

• 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.