Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models

Abstract

The Sachdev-Ye-Kitaev model is a $(0+1)$-dimensional model describing Majorana fermions or complex fermions with random interactions. This model has various interesting properties such as approximate local criticality (power law correlation in time), zero temperature entropy, and quantum chaos. In this article, we propose a higher dimensional generalization of the Sachdev-Ye-Kitaev model, which is a lattice model with $N$ Majorana fermions at each site and random interactions between them. Our model can be defined on arbitrary lattices in arbitrary spatial dimensions. In the large $N$ limit, the higher dimensional model preserves many properties of the Sachdev-Ye-Kitaev model such as local criticality in two-point functions, zero temperature entropy and chaos measured by the out-of-time-ordered correlation functions. In addition, we obtain new properties unique to higher dimensions such as diffusive energy transport and a "butterfly velocity" describing the propagation of chaos in space. We mainly present results for a $(1+1)$-dimensional example, and discuss the general case near the end.

1+37 pages, published version

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• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
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• Bosonic Tensor Models at Large $N$ and Small $\epsilon$
• An upper bound on transport
• Effective Field Theory for Chaotic CFTs
• Black hole on a chip: proposal for a physical realization of the SYK model in a solid-state system
• Disentangling Scrambling and Decoherence via Quantum Teleportation
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• Expanding the Black Hole Interior: Partially Entangled Thermal States in SYK
• Quantum Entanglement of the Sachdev-Ye-Kitaev Models
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• A Holographic Derivation of the Weak Gravity Conjecture
• Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models
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• Random Matrices and Holographic Tensor Models
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• Emergent Replica Conformal Symmetry in Non-Hermitian SYK${}_2$ Chains
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• The double scaled limit of Super--Symmetric SYK models
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• Loop current fluctuations and quantum critical transport
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• Phases Of Melonic Quantum Mechanics
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• Slow relaxation and diffusion in holographic quantum critical phases
• Holographic chaos, pole-skipping, and regularity
• Fine-Grained Chaos in $Ad{S}_2$ Gravity
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• Dynamical quantum phase transitions in SYK Lindbladians
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• Comments on the Random Thirring Model
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• On thermalization in the SYK and supersymmetric SYK models
• Yukawa-SYK model and Self-tuned Quantum Criticality
• Topological Sachdev-Ye-Kitaev Model
• Thermal Diffusion and Quantum Chaos in Neutral Magnetized Plasma
• Replica-nondiagonal solutions in the SYK model
• Quenched vs Annealed: Glassiness from SK to SYK
• Complex Sachdev-Ye-Kitaev model in the double scaling limit
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• Effective dimension, level statistics, and integrability of Sachdev-Ye-Kitaev-like models
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• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
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• A candidate Theory for the "Strange Metal" phase at Finite Energy Window
• Supersymmetry in the nonsupersymmetric Sachdev-Ye-Kitaev model
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• Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models
• Weyl corrections to diffusion and chaos in holography
• Many-Body Localization in a finite-range Sachdev-Ye-Kitaev model
• Quantum Scrambling and State Dependence of the Butterfly Velocity
• On the replica structure of Sachdev-Ye-Kitaev model
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• Charged BTZ-like black hole solutions and the diffusivity-butterfly velocity relation
• Speeding up the spread of quantum information in chaotic systems
• Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$
• Many-body chaos near a thermal phase transition
• Chiral Algebras of Two-Dimensional SYK Models
• Scrambling with conservation law
• Quasinormal modes of a semi-holographic black brane and thermalization
• Quantum steering as a witness of quantum scrambling
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• Thermal effects in non-Fermi liquid superconductivity
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• Strongly coupled phonon fluid and Goldstone modes in an anharmonic quantum solid: transport and chaos
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• Quantum information scrambling and quantum chaos in little string theory
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• An Inelastic Bound on Chaos
• Out-of-Time-Order Correlators in One-Dimensional XY model
• Quantum Information Scrambling Through a High-Complexity Operator Mapping
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• Schwarzian correction to quantum correlation in SYK model
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• Violation of the viscosity/entropy bound in translationally invariant non-Fermi liquids
• Sparse random matrices and Gaussian ensembles with varying randomness
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• Thermalization of Randomly Coupled SYK Models
• Transport properties of an interacting Majorana chain
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• Sachdev-Ye-Kitaev type physics in the strained Kitaev honeycomb model
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• Slow scrambling and hidden integrability in a random rotor model
• Operator size growth in Lindbladian SYK
• A classical model for sub-Planckian thermal diffusivity in complex crystals
• Quantum circuits with classically simulable operator scrambling
• Pole-skipping of Holographic Correlators: Aspects of Gauge Symmetry and Generalizations
• Many-body chaos in the antiferromagnetic quantum critical metal
• Multiway Junction Conditions: Booklets and Webs
• Holographic study of shear viscosity and butterfly velocity for magnetic field-driven quantum criticality
• Bulk Reconstruction from Generalized Free Fields
• Factorizing Wormholes in a Partially Disorder-Averaged SYK Model
• Toward the nonequilibrium thermodynamic analog of complexity and the Jarzynski identity
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• Entanglement inside a black hole before the Page time
• Thermalization of a Closed Sachdev-Ye-Kitaev System in the Thermodynamic Limit
• Nematic phases and elastoresistivity from a multiorbital non-Fermi liquid
• Field theory for monitored Brownian SYK clusters
• Wormhole-induced effective coupling in SYK chains
• SYK does not Transit Gloria Mundi just yet
• Phase space holography with no strings attached
• Operator growth and black hole formation
• Charge fluctuation entropy of Hawking radiation: a replica-free way to find large entropy
• Size Winding Mechanism beyond Maximal Chaos
• Traveling discontinuity at the quantum butterfly front
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• Scrambling Transition in Free Fermion Systems Induced by a Single Impurity
• Super-maximal chaos and instability
• Random coupling model of turbulence as a classical Sachdev-Ye-Kitaev model
• The chiral SYK model in three-dimensional holography
• SYK model based $\beta$ regime dependent two-qubit dynamical wormhole-inspired teleportation protocol simulation
• Current Correlations and Conductivity in SYK-Like Systems: An Analytical Study
• Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions
• Directional scrambling of quantum information in helical multiferroics
• Slowest and Fastest Information Scrambling in the Strongly Disordered XXZ Model
• Statistical Mechanics of Exponentially Many Low Lying States
• Attenuating Dynamics of Strongly Interacting Fermionic Superfluids in SYK Solvable Models
• Kinetics of information scrambling in correlated electrons: disorder-driven transition from shock-wave to FKPP dynamics
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos
• Energy dynamics in a class of local random matrix Hamiltonians
• The extended diffusive Sachdev-Ye-Kitaev model as a sort of "strange metal"
• Eigenstate Thermalization in the Two-Site SYK and SYK Chain Models
• Information scrambling of the dilute Bose gas at low temperature
• Information scrambling and butterfly velocity in quantum spin glass chains
• Universal thermalization dynamics in (1+1)d QFTs
• Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
• Phase Thermalization: from Fermi Liquid to Incoherent Metal
• Symmetry resolved out-of-time-order correlators of Heisenberg spin chains using projected matrix product operators
• Operator delocalization in disordered spin chains via exact MPO marginals
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models
• Probing Stringy Horizons with Pole-Skipping in Non-Maximal Chaotic Systems
• Realizing Unitary $k$-designs with a Single Quench
• Fold bifurcation entangled surfaces for one-dimensional Kitaev lattice model
• Quasiparticle tunnelling in two coupled chiral SYK model
• Entanglement production in the Sachdev-Ye-Kitaev Model and its variants
• Correlation Functions and Chaotic Behavior of the SYK Chain Model in Pure States
• Quantum entropy thermalization