Non-ergodic delocalized phase with Poisson level statistics

@article{Tang2021NonergodicDP,
  title={Non-ergodic delocalized phase with Poisson level statistics},
  author={Weichen Tang and Ivan M Khaymovich},
  journal={Quantum},
  year={2021},
  volume={6},
  pages={733}
}
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… 

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References

SHOWING 1-10 OF 78 REFERENCES

Many-body localization phase transition

We use exact diagonalization to explore the many-body localization transition in a random-field spin-1/2 chain. We examine the correlations within each many-body eigenstate, looking at all

Multifractal Scalings Across the Many-Body Localization Transition.

Using exact diagonalization techniques, this Letter addresses the ergodicity properties in the underlying N-dimensional complex networks spanned by various computational bases for up to L=24 spin-1/2 particles, and reports fully ergodic eigenstates in the delocalized phase (irrespective of the computational basis).

Delocalized glassy dynamics and many-body localization

We analyze the unusual slow dynamics that emerges in the bad metal delocalized phase preceding the Many-Body Localization transition by using single-particle Anderson Localization on the Bethe

A random matrix model with localization and ergodic transitions

Motivated by the problem of many-body localization and the recent numerical results for the level and eigenfunction statistics on the random regular graphs, a generalization of the Rosenzweig–Porter

Emergent fractal phase in energy stratified random models

We study the effects of partial correlations in kinetic hopping terms of long-range disordered random matrix models on their localization properties. We consider a set of models interpolating between

Duality in Power-Law Localization in Disordered One-Dimensional Systems.

This model is an example of a new universality class of models with power-law hopping, characterized by a duality between systems with long-range hops and short-range hopping, in which the wave function amplitude falls off algebraically with the same power γ from the localization center.

Unbounded growth of entanglement in models of many-body localization.

The significance for proposed atomic experiments is that local measurements will show a large but nonthermal entropy in the many-body localized state, which develops slowly over a diverging time scale as in glassy systems.

Many-body localization transition in Hilbert space

In this paper we propose a new perspective to analyze the many-body localization (MBL) transition when recast in terms of a single-particle tight-binding model in the space of many-body

Renormalization to localization without a small parameter

We study the wave function localization properties in a d-dimensional model of randomly spaced particles with isotropic hopping potential depending solely on Euclidean interparticle distances. Due to

Entanglement of midspectrum eigenstates of chaotic many-body systems: Reasons for deviation from random ensembles.

Eigenstates of local many-body interacting systems that are far from spectral edges are thought to be ergodic and close to being random states. This is consistent with the eigenstate thermalization
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