Spectral statistics across the many-body localization transition

By Maksym Serbyn, J. Moore. 2015

162 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/564ef5d880626fa93b4e279ef88a89a54222665d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. V. Ros
2. J. Imbrie
3. Antonello Scardicchio
4. Tomaz Prosen
5. L. Vidmar
6. Romain Vasseur
7. J. Bonvca
8. Jan vSuntajs

In Condensed Matter Physics

1. Tomaz Prosen
2. Antonello Scardicchio
3. L. Vidmar
4. J. Bonvca
5. Jan vSuntajs
6. V. Ros
7. J. Imbrie
8. Romain Vasseur

In Statistical and Nonlinear Physics

1. Tomaz Prosen
2. L. Vidmar
3. Romain Vasseur
4. Antonello Scardicchio
5. J. Bonvca
6. Jan vSuntajs
7. V. Ros
8. J. Imbrie

Citations in the corpus

• Nonequilibrium quantum dynamics and transport: from integrability to many-body localization (2016, background): “Among the most challenging and controversial questions are the nature of the level statistics at the critical point [130, 131], the existence of an intermediate phase that would be delocalized but non-ergodic [132, 133, 134, 135], the scaling of the eigenstate entanglement entropy in the critical fa”
• Ergodicity breaking transition in finite disordered spin chains (2020, methodology): “MBL and the corresponding transition were widely studied by means of numerical approaches [35, 45–73] and phenomenological theories [74–85], as well as experimentally [86–92].”
• Local integrals of motion in many‐body localized systems (2016, background): “Starting from the earlier works [9, 18], the absence of level repulsion, generically regarded as a signature of integrability [19, 20, 84], has been extensively exploited as a characterization of the MBL phase, see also [9, 23, 30, 70, 80, 93].”
• Many-body localization: An introduction and selected topics (2017, unknown): “…states can be efficiently represented by matrix product states (MPS) in one dimension, providing a very useful numerical arsenal for capturing highly-excited states, something which is usually not possible (see Section 3.9) (iii) It was actually proposed that a proper definition of a MBL state is that”