# Spectral statistics across the many-body localization transition

@article{Serbyn2016SpectralSA, title={Spectral statistics across the many-body localization transition}, author={Maksym Serbyn and Joel E Moore}, journal={Physical Review B}, year={2016}, volume={93}, pages={041424} }

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… Expand

#### 108 Citations

Statistics of correlations across the many-body localization transition

- Mathematics, Physics
- 2019

Ergodic quantum many-body systems satisfy the eigenstate thermalization hypothesis (ETH). However, strong disorder can destroy ergodicity through many-body localization (MBL) – at least in one… Expand

Level statistics across the many-body localization transition

- Physics, Computer Science
- Physical Review B
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It is argued that the transition in the case of random disorder exhibits universal features that are identified by constructing an appropriate model of intermediate spectral statistics which is a generalization of the family of short-range plasma models. Expand

Many-Body-Localization Transition in the Strong Disorder Limit: Entanglement Entropy from the Statistics of Rare Extensive Resonances

- Physics, Computer Science
- Entropy
- 2016

This paper considers the strong disorder limit of the MBL transition, where the critical level statistics is close to the Poisson statistics, and explains why for the Many-Body-Localization transition concerning individual eigenstates, the correlation length exponent is not constrained by the usual Harris inequality. Expand

On intermediate statistics across many-body localization transition

- Physics
- Journal of Physics A: Mathematical and Theoretical
- 2021

The level statistics in the transition between delocalized and localized {phases of} many body interacting systems is {considered}. We recall the joint probability distribution for eigenvalues… Expand

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- Physics
- 2020

Disordered interacting spin chains that undergo a many-body localization transition are characterized by two limiting behaviors where the dynamics are chaotic and integrable. However, the transition… Expand

Thouless energy and multifractality across the many-body localization transition

- Physics
- 2017

Thermal and many-body localized phases are separated by a dynamical phase transition of a new kind. We analyze the distribution of off-diagonal matrix elements of local operators across this… Expand

Energy diffusion in the ergodic phase of a many body localizable spin chain

- Physics
- 2015

The phenomenon of many-body localization in disordered quantum many-body systems occurs when all transport is suppressed despite the fact that the excitations of the system interact. In this work we… Expand

Many-body-localization transition: strong multifractality spectrum for matrix elements of local operators

- Physics, Mathematics
- 2016

For short-ranged disordered quantum models in one dimension, the Many-Body-Localization is analyzed via the adaptation to the Many-Body context [M. Serbyn, Z. Papic and D.A. Abanin, PRX 5, 041047… Expand

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We numerically study level statistics of disordered interacting quantum many-body systems. A two-parameter plasma model which controls the level repulsion exponent $\ensuremath{\beta}$ and range $h$… Expand

Many-body localization in Fock space: A local perspective

- Physics
- Physical Review B
- 2019

A canonical model for many-body localization (MBL) is studied, of interacting spinless fermions on a lattice with uncorrelated quenched site-disorder. The model maps onto a tight-binding model on a… Expand

#### References

SHOWING 1-10 OF 41 REFERENCES

Criterion for Many-Body Localization-Delocalization Phase Transition

- Physics
- 2015

We propose a new approach to probing ergodicity and its breakdown in one-dimensional quantum many-body systems based on their response to a local perturbation. We study the distribution of matrix… Expand

Theory of the many-body localization transition in one dimensional systems

- Physics
- 2014

We formulate a theory of the many-body localization transition based on a novel real space renormalization group (RG) approach. The results of this theory are corroborated and intuitively explained… Expand

Total correlations of the diagonal ensemble herald the many-body localization transition

- Physics
- 2015

The intriguing phenomenon of many-body localization (MBL) has attracted significant interest recently, but a complete characterization is still lacking. In this work, we introduce the total… Expand

Statistics of energy levels and eigenfunctions in disordered systems

- Physics
- 2000

Abstract The article reviews recent developments in the theory of fluctuations and correlations of energy levels and eigenfunction amplitudes in diffusive mesoscopic samples. Various spatial… Expand

Dynamics at the Many-Body Localization Transition

- Physics
- 2015

Above a critical disorder strength, localization occurs al so in systems with interaction. Among the latter, the one-dimensional isolated Heisenberg model with random static magnetic fields has… Expand

Anomalous diffusion and griffiths effects near the many-body localization transition.

- Physics, Medicine
- Physical review letters
- 2015

This work explores the high-temperature dynamics of the disordered, one-dimensional XXZ model near the many-body localization (MBL) transition, focusing on the delocalized (i.e., "metallic") phase, and establishes scaling relations between the associated exponents, assuming a scaling form of the spin-diffusion propagator. Expand

Localization of interacting fermions at high temperature

- Physics
- 2007

We suggest that if a localized phase at nonzero temperature $Tg0$ exists for strongly disordered and weakly interacting electrons, as recently argued, it will also occur when both disorder and… Expand

Many-body localization phase transition

- Physics
- 2010

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… Expand

Effective plasma model for the level correlations at the mobility edge

- Physics
- 1995

We consider the mapping of the energy level statistics for a d-dimensional disordered electron system at the mobility edge between metallic and insulating phases onto the model of a classical… Expand

Critical statistics in quantum chaos and Calogero-Sutherland model at finite temperature.

- Mathematics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2003

It is shown that the number variance of the random matrix model is asymptotically linear with a slope depending on the parameters of the model, a signature of critical statistics. Expand