Non-ergodic delocalized phase with Poisson level statistics

Weichen Tang; Ivan M. Khaymovich

doi:10.22331/q-2022-06-09-733

Non-ergodic delocalized phase with Poisson level statistics

Weichen Tang¹ and Ivan M. Khaymovich^2,3,4

¹Department of Physics, University of California, Berkeley, California 94720, USA
²Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Straße 38, 01187-Dresden, Germany
³Institute for Physics of Microstructures, Russian Academy of Sciences, 603950 Nizhny Novgorod, GSP-105, Russia
⁴Nordita, Stockholm University and KTH Royal Institute of Technology Hannes Alfvéns väg 12, SE-106 91 Stockholm, Sweden

Published:	2022-06-09, volume 6, page 733
Eprint:	arXiv:2112.09700v4
Doi:	https://doi.org/10.22331/q-2022-06-09-733
Citation:	Quantum 6, 733 (2022).

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24 pages, 6 figures, 73 references + 3 pages in Appendix, accepted to Quantum journal

Abstract

Motivated by the many-body localization (MBL) phase in generic interacting disordered quantum systems, we develop a model simulating the same eigenstate structure like in MBL, but in the random-matrix setting. Demonstrating the absence of energy level repulsion (Poisson statistics), this model carries non-ergodic eigenstates, delocalized over the extensive number of configurations in the Hilbert space. On the above example, we formulate general conditions to a single-particle and random-matrix models in order to carry such states, based on the transparent generalization of the Anderson localization of single-particle states and multiple resonances.

Featured image: Motivated by the many-body localization phase, we develop a random-matrix model simulating the same eigenstate structure. In order to have multifractal delocalized state without level repulsion we combine a power-law decaying hopping with the amplitude scaling up with the matrix size with respect to the diagonal disorder. This makes the multiple resonances possible without leading to level repulsion.

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Popular summary

Many-body localization is a phenomenon, providing a unique possibility for an isolated interacting quantum system to avoid thermalization and to keep the information about its initial state.
Being the localization in the real space, many-body localization not only suppresses the transport, but also avoids repulsion of energy levels and makes eigenstates of an interacting system to be non-ergodic, but extended in the space of configurations (Hilbert space).
Facing the difficulties of describing many-body quantum systems, many researchers focus on the universal statistical description of the above phenomenon in a random-matrix setting.

Motivated by the many-body localization phase, we develop a random-matrix model simulating the same eigenstate structure.
Demonstrating the absence of energy level repulsion (Poisson statistics), this model carries non-ergodic eigenstates, delocalized over the extensive number of configurations in the Hilbert space.
Using the above example and a transparent generalization of the Anderson localization to multiple resonances, we formulate general conditions to realize non-ergodic states with Poisson level statistics.

► BibTeX data

@article{Tang2022nonergodic,
  doi = {10.22331/q-2022-06-09-733},
  url = {https://doi.org/10.22331/q-2022-06-09-733},
  title = {Non-ergodic delocalized phase with {P}oisson level statistics},
  author = {Tang, Weichen and Khaymovich, Ivan M.},
  journal = {{Quantum}},
  issn = {2521-327X},
  publisher = {{Verein zur F{\"{o}}rderung des Open Access Publizierens in den Quantenwissenschaften}},
  volume = {6},
  pages = {733},
  month = jun,
  year = {2022}
}

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