Many-Body Chaos in the Sachdev-Ye-Kitaev Model

Abstract

Many-body chaos has emerged as a powerful framework for understanding thermalization in strongly interacting quantum systems. While recent analytic advances have sharpened our intuition for many-body chaos in certain large $N$ theories, it has proven challenging to develop precise numerical tools capable of exploring this phenomenon in generic Hamiltonians. To this end, we utilize massively parallel, matrix-free Krylov subspace methods to calculate dynamical correlators in the Sachdev-Ye-Kitaev (SYK) model for up to $N=60$ Majorana fermions. We begin by showing that numerical results for two-point correlation functions agree at high temperatures with dynamical mean field solutions, while at low temperatures finite-size corrections are quantitatively reproduced by the exactly solvable dynamics of near extremal black holes. Motivated by these results, we develop a novel finite-size rescaling procedure for analyzing the growth of out-of-time-order correlators (OTOCs). We verify that this procedure accurately determines the Lyapunov exponent, $\lambda$, across a wide range in temperatures, including in the regime where $\lambda$ approaches the universal bound, $\lambda =2\pi /\beta$.

6+15 pages, 3+11 figures. v3 published version, with corrected prefactor in Eq. 1

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• Beneficial and detrimental entanglement for quantum battery charging
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• Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments
• Semiclassical roots of universality in many-body quantum chaos
• Excitation spectra of quantum matter without quasiparticles I: Sachdev-Ye-Kitaev models
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• Keldysh Wormholes and Anomalous Relaxation in the Dissipative Sachdev-Ye-Kitaev Model
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
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• Toward simulating Superstring/M-theory on a quantum computer
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• Sachdev-Ye-Kitaev model on a noisy quantum computer
• Scrambling versus relaxation in Fermi and non-Fermi liquids
• Multifractality in quasienergy space of coherent states as a signature of quantum chaos
• The Weak Gravity Conjecture Requires the Existence of Exotic AdS Black Holes
• Stabilizer Entropy and entanglement complexity in the Sachdev-Ye-Kitaev model
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• Subleading Bounds on Chaos
• Proposal for measuring out-of-time-ordered correlators at finite temperature with coupled spin chains
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• Can neural quantum states learn volume-law ground states?
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• Extremal Chaos
• Sachdev-Ye-Kitaev circuits for braiding and charging Majorana zero modes
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• Dynamical transition from localized to uniform scrambling in locally hyperbolic systems
• Brickwall One-Loop Determinant: Spectral Statistics & Krylov Complexity
• Strongly coupled phonon fluid and Goldstone modes in an anharmonic quantum solid: transport and chaos
• Quantum Chaos in the Extended Dicke Model
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• Sparse random matrices and Gaussian ensembles with varying randomness
• On Quantum Simulation Of Cosmic Inflation
• Analyticity constraints bound the decay of the spectral form factor
• Quantum Chaos and Circuit Parameter Optimization
• Fermionic Isometric Tensor Network States in Two Dimensions
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• Excitation Transmission through a non-Hermitian traversable wormhole
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• Operator growth and black hole formation
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• Quantum Annealing with chaotic driver Hamiltonians
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• SYK model based $\beta$ regime dependent two-qubit dynamical wormhole-inspired teleportation protocol simulation
• Quantum simulations of complex systems
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• Sparse SYK and traversable wormholes
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