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Many-Body Level Statistics of Single-Particle Quantum Chaos

Journal Article · · Physical Review Letters
We consider a noninteracting many-fermion system populating levels of a unitary random matrix ensemble (equivalent to the q = 2 complex Sachdev-Ye-Kitaev model)—a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form factor, which we show to be a universal feature of nonergodic many-fermion systems embedded in a chaotic medium.
Research Organization:
University of Maryland, College Park, MD (United States)
Sponsoring Organization:
USDOE Office of Science (SC)
Grant/Contract Number:
SC0001911
OSTI ID:
1850765
Journal Information:
Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 25 Vol. 125; ISSN 0031-9007; ISSN PRLTAO
Publisher:
American Physical Society (APS)Copyright Statement
Country of Publication:
United States
Language:
English

References (51)

Quantum Signatures of Chaos book January 2010
On the connection between quantization of nonintegrable systems and statistical theory of spectra journal June 1980
Black holes and random matrices journal May 2017
The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual journal May 2018
Chaos and random matrices in supersymmetric SYK journal May 2018
The Thouless time for mass-deformed SYK journal September 2018
Chaos, complexity, and random matrices journal November 2017
On Many-Body Localization for Quantum Spin Chains journal April 2016
Quantizing a classically ergodic system: Sinai's billiard and the KKR method journal January 1981
On the distribution of the total energy of a system of non-interacting fermions: random matrix and semiclassical estimates journal July 1999
Metal–insulator transition in a weakly interacting many-electron system with localized single-particle states journal May 2006
Quantum ergodicity in the SYK model journal May 2018
Randomness and chaos in qubit models journal August 2019
Thermalization and its mechanism for generic isolated quantum systems journal April 2008
Quantum chaos in ultracold collisions of gas-phase erbium atoms journal March 2014
Quantum chaos and breaking of all anti-unitary symmetries in Rydberg excitons journal April 2016
The Lyapunov spectra of quantum thermalisation journal June 2019
Statistical Theory of the Energy Levels of Complex Systems. I journal January 1962
Signatures of quantum chaos in the magneto-excitonic spectrum of quantum wells journal February 1998
From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics journal May 2016
Supersymmetry and theory of disordered metals journal January 1983
Critique of the replica trick journal May 1985
Wigner-Dyson statistics from the replica method journal January 1999
The approach to thermal equilibrium in quantized chaotic systems journal January 1999
Spectral statistics of chaotic many-body systems journal March 2016
Semiclassical theory of spectral rigidity journal August 1985
Universal level statistics of the out-of-time-ordered operator journal July 2019
Level correlations in disordered metals: The replica σ model journal August 1999
Localization of interacting fermions at high temperature journal April 2007
Possible experimental manifestations of the many-body localization journal August 2007
Many-body delocalization transition and relaxation in a quantum dot journal March 2016
Sachdev-Ye-Kitaev model and thermalization on the boundary of many-body localized fermionic symmetry-protected topological states journal March 2017
Remarks on the Sachdev-Ye-Kitaev model journal November 2016
Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model journal December 2016
Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model journal May 2018
Spectral form factors and late time quantum chaos journal October 2018
Chaos and quantum thermalization journal August 1994
Magnetic Field Control of the Quantum Chaotic Dynamics of Hydrogen Analogs in an Anisotropic Crystal Field journal July 2010
Exact Spectral Form Factor in a Minimal Model of Many-Body Quantum Chaos journal December 2018
Nonergodic Extended States in the Sachdev-Ye-Kitaev Model journal September 2019
Bounds on Chaos from the Eigenstate Thermalization Hypothesis journal December 2019
Exponential Ramp in the Quadratic Sachdev-Ye-Kitaev Model journal December 2020
Spectrum and Eigenfunctions for a Hamiltonian with Stochastic Trajectories journal April 1979
Characterization of Chaotic Quantum Spectra and Universality of Level Fluctuation Laws journal January 1984
Onset of chaos in rapidly rotating nuclei journal June 1990
Emergence of Quantum Chaos in Finite Interacting Fermi Systems journal September 1997
Wigner-Dyson Statistics from the Keldysh σ -Model journal December 2000
Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory journal June 2018
Random matrices and chaos in nuclear physics: Nuclear reactions journal October 2010
Colloquium : Many-body localization, thermalization, and entanglement journal May 2019
Many-Body Localization and Thermalization in Quantum Statistical Mechanics journal March 2015

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