Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev Model

Abstract

We investigate the supersymmetric Sachdev-Ye-Kitaev (SYK) model, $N$ Majorana fermions with infinite range interactions in $0+1$ dimensions. We have found that, close to the ground state $E\approx 0$, discrete symmetries alter qualitatively the spectral properties with respect to the non-supersymmetric SYK model. The average spectral density at finite $N$, which we compute analytically and numerically, grows exponentially with $N$ for $E\approx 0$. However the chiral condensate, which is normalized with respect the total number of eigenvalues, vanishes in the thermodynamic limit. Slightly above $E\approx 0$, the spectral density grows exponential with the energy. Deep in the quantum regime, corresponding to the first $O(N)$ eigenvalues, the average spectral density is universal and well described by random matrix ensembles with chiral and superconducting discrete symmetries. The dynamics for $E\approx 0$ is investigated by level fluctuations. Also in this case we find excellent agreement with the prediction of chiral and superconducting random matrix ensembles for eigenvalues separations smaller than the Thouless energy, which seems to scale linearly with $N$. Deviations beyond the Thouless energy, which describes how ergodicity is approached, are universality characterized by a quadratic growth of the number variance. In the time domain, we have found analytically that the spectral form factor $g(t)$, obtained from the connected two-level correlation function of the unfolded spectrum, decays as $1/t^2$ for times shorter but comparable to the Thouless time with $g(0)$ related to the coefficient of the quadratic growth of the number variance. Our results provide further support that quantum black holes are ergodic and therefore can be classified by random matrix theory.

24 pages, 6 figures, added references

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Cited by in corpus (51)

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• Many-body level statistics of single-particle quantum chaos
• Thouless time for mass-deformed SYK
• The double scaled limit of Super--Symmetric SYK models
• Phases Of Melonic Quantum Mechanics
• From operator statistics to wormholes
• Periodic Table of SYK and supersymmetric SYK
• Spectral Fluctuations in the Sachdev-Ye-Kitaev Model
• Krylov Complexity and Spectral Form Factor for Noisy Random Matrix Models
• Delayed Thermalization in Mass-Deformed SYK
• Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models
• Universality and its limits in non-Hermitian many-body quantum chaos using the Sachdev-Ye-Kitaev model
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• The tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model
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• Emergence of many-body quantum chaos via spontaneous breaking of unitarity
• On the Spectral Form Factor for Random Matrices
• $T\overline{T}$ Deformations of Supersymmetric Quantum Mechanics
• Probing the metallic energy spectrum beyond the Thouless energy scale using the singular value decomposition
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• Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs
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• Probing quantum chaos through singular-value correlations in sparse non-Hermitian SYK model
• Toward a classification of PT-symmetric quantum systems: From dissipative dynamics to topology and wormholes
• Large scale behavior of the energy spectra of the quantum random antiferromagnetic Ising chain with mixed transverse and longitudinal fields
• Complete Solution of a Gauged Tensor Model
• Average-fluctuation separation in energy levels in many-particle quantum systems with $k$-body interactions using $q$-Hermite polynomials
• Structure of wavefunction for interacting bosons in mean-field with random $k$-body interactions
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• Superconducting gap ratio from strange metal phase in the absence of quasiparticles
• Statistical Nuclear Spectroscopy with $q$-normal and bivariate $q$-normal distributions and $q$-Hermite polynomials
• Emergent Topology in Many-Body Dissipative Quantum Matter
• Quantum Chaos, Thermodynamics and Black Hole Microstates in the mass deformed SYK model
• Spectrum of SYK model II: Central limit theorem
• Thermalization in many-fermion quantum systems with one- plus random $k$-body interactions
• Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model
• Bivariate moments of the two-point correlation function for embedded Gaussian unitary ensemble with $k$-body interactions
• Janossy densities for chiral random matrix ensembles and their applications to two-color QCD
• Anatomy of information scrambling and decoherence in the integrable Sachdev-Ye-Kitaev model
• Spectrum of SYK model III: Large deviations and concentration of measures
• A route from maximal chaoticity to integrability
• Eigenstate Thermalization in the Two-Site SYK and SYK Chain Models
• Replica Symmetry Breaking in Random Non-Hermitian Systems
• Correlation Functions and Chaotic Behavior of the SYK Chain Model in Pure States