D-commuting SYK model: building quantum chaos from integrable blocks

Abstract

We construct a new family of quantum chaotic models by combining multiple copies of integrable commuting SYK models. As each copy of the commuting SYK model does not commute with others, this construction breaks the integrability of each commuting SYK and the family of models demonstrates the emergence of quantum chaos. We study the spectrum of this model analytically in the double-scaled limit. As the number of copies tends to infinity, the spectrum becomes compact and equivalent to the regular SYK model. For finite $d$ copies, the spectrum is close to the regular SYK model in UV but has an exponential tail $e^{E/T_c}$ in the IR. We identify the reciprocal of the exponent in the tail as a critical temperature $T_c$, above which the model should be quantum chaotic. $T_c$ monotonically decreases as $d$ increases, which expands the chaotic regime over the non-chaotic regime. We propose the existence of a new phase around $T_c$, and the dynamics should be very different in two phases. We further carry out numeric analysis at finite $d$, which supports our proposal. Given any finite dimensional local Hamiltonian, by decomposing it into $d$ groups, in which all terms in one group commute with each other but terms from different groups may not, our analysis can give an estimate of the critical temperature for quantum chaos based on the decomposition. We also comment on the implication of the critical temperature to future quantum simulations of quantum chaos and quantum gravity.

27 pages plus appendix, 16 figures, 2 tables

References in corpus (31)

• A bound on chaos
• Comments on the Sachdev-Ye-Kitaev model
• Black holes and the butterfly effect
• Localized shocks
• Black Holes and Random Matrices
• Traversable Wormholes via a Double Trace Deformation
• Fermionic Localization of the Schwarzian Theory
• Does scrambling equal chaos?
• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• Towards a full solution of the large N double-scaled SYK model
• Digital Quantum Simulation of Minimal AdS/CFT
• Creating and probing the Sachdev-Ye-Kitaev model with ultracold gases: Towards experimental studies of quantum gravity
• Many-Body Chaos in the Sachdev-Ye-Kitaev Model
• Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction
• Quantum holography in a graphene flake with an irregular boundary
• Phase Transition in the Density of States of Quantum Spin Glasses
• Exponential growth of out-of-time-order correlator without chaos: inverted harmonic oscillator
• Black hole on a chip: proposal for a physical realization of the SYK model in a solid-state system
• Sparse Sachdev-Ye-Kitaev model, quantum chaos and gravity duals
• Early-Time Exponential Instabilities in Non-Chaotic Quantum Systems
• A symmetry algebra in double-scaled SYK
• Many-body quantum teleportation via operator spreading in the traversable wormhole protocol
• Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model
• Vector models and generalized SYK models
• Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Quantum chaos without false positives
• Refined quantum Lyapunov exponents from replica out-of-time-order correlators
• Engineering SYK interactions in disordered graphene flakes under realistic experimental conditions
• Disordered vector models: from higher spins to incipient strings
• A supersymmetric SYK model with a curious low energy behavior

Cited by in corpus (1)

• Free Probability approach to spectral and operator statistics in Rosenzweig-Porter random matrix ensembles