Spectral statistics across the many-body localization transition

M. Serbyn, J. Moore, Physical Review B - Condensed Matter and Materials Physics 93 (2016).


Journal Article | Published
Author
Serbyn, MaksymIST Austria ; Moore, Joel E
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.
Publishing Year
Date Published
2016-01-29
Journal Title
Physical Review B - Condensed Matter and Materials Physics
Volume
93
Issue
4
IST-REx-ID
986

Cite this

Serbyn M, Moore J. Spectral statistics across the many-body localization transition. Physical Review B - Condensed Matter and Materials Physics. 2016;93(4). doi:10.1103/PhysRevB.93.041424
Serbyn, M., & Moore, J. (2016). Spectral statistics across the many-body localization transition. Physical Review B - Condensed Matter and Materials Physics, 93(4). https://doi.org/10.1103/PhysRevB.93.041424
Serbyn, Maksym, and Joel Moore. “Spectral Statistics across the Many-Body Localization Transition.” Physical Review B - Condensed Matter and Materials Physics 93, no. 4 (2016). https://doi.org/10.1103/PhysRevB.93.041424.
M. Serbyn and J. Moore, “Spectral statistics across the many-body localization transition,” Physical Review B - Condensed Matter and Materials Physics, vol. 93, no. 4, 2016.
Serbyn M, Moore J. 2016. Spectral statistics across the many-body localization transition. Physical Review B - Condensed Matter and Materials Physics. 93(4).
Serbyn, Maksym, and Joel Moore. “Spectral Statistics across the Many-Body Localization Transition.” Physical Review B - Condensed Matter and Materials Physics, vol. 93, no. 4, American Physical Society, 2016, doi:10.1103/PhysRevB.93.041424.
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