Non-ergodic delocalized phase with Poisson level statistics

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.

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

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• Sub-diffusive Thouless time scaling in the Anderson model on random regular graphs
• Nonperturbative theory of power spectrum in complex systems
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• Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices
• Diagnostics of nonergodic extended states and many body localization proximity effect through real-space and Fock-space excitations
• Multifractal phase in the weighted adjacency matrices of random Erdös-Rényi graphs
• Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions
• Quasiperiodicity hinders ergodic Floquet eigenstates
• Robust non-ergodicity of ground state in the $\beta$ ensemble
• Anatomy of the eigenstates distribution: a quest for a genuine multifractality
• Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems
• Multifractality in the interacting disordered Tavis-Cummings model
• Many-body localization proximity effect in two-species bosonic Hubbard model
• Emergent multifractality in power-law decaying eigenstates
• Re-entrant localization induced by short-range hopping in the fractal Rosenzweig-Porter Model
• Superdiffusion in random two dimensional system with time-reversal symmetry and long-range hopping
• Refined cyclic renormalization group in Russian Doll model
• The Wishart--Rosenzweig--Porter random matrix ensemble
• Coexistence of localized and extended states in the Anderson model with long-range hopping
• Ergodicity-breaking phase diagram and fractal dimensions in long-range models with generically correlated disorder
• Replica approach to the generalized Rosenzweig-Porter model
• Localization and fractality in disordered Russian Doll model