Sachdev-Ye-Kitaev Model as Liouville Quantum Mechanics

Abstract

We show that the proper inclusion of soft reparameterization modes in the Sachdev-Ye-Kitaev model of $N$ randomly interacting Majorana fermions reduces its long-time behavior to that of Liouville quantum mechanics. As a result, all zero temperature correlation functions decay with the universal exponent $\propto {\tau }^{-3/2}$ for times larger than the inverse single particle level spacing $\tau \gg N\ln N$. In the particular case of the single particle Green function this behavior is manifestation of the zero-bias anomaly, or scaling in energy as ${\epsilon }^{1/2}$. We also present exact diagonalization study supporting our conclusions.

arXiv comment14 pages, 2 figures

References in corpus (11)

• Comments on the Sachdev-Ye-Kitaev model
• Structure Constants and Conformal Bootstrap in Liouville Field Theory
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Bekenstein-Hawking Entropy and Strange Metals
• Liouville theory revisited
• Liouville Field Theory -- A decade after the revolution
• Electron--electron Interactions in Disordered Metals: Keldysh Formalism
• Delocalization Transition via Supersymmetry in one Dimension
• The Liouville Theory as a Model for Prelocalized States in Disordered Conductors
• Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space
• An Effective Theory for Midgap States in Doped Spin Ladder and Spin-Peierls Systems: Liouville Quantum Mechanics

Cited by in corpus (208)

• Black Holes and Random Matrices
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Thermoelectric transport in disordered metals without quasiparticles: the SYK models and holography
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Fermionic Localization of the Schwarzian Theory
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• A Generalization of Sachdev-Ye-Kitaev
• Solving the Schwarzian via the Conformal Bootstrap
• Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids
• Solvable model for a dynamical quantum phase transition from fast to slow scrambling
• AdS${}_2$ holography and the SYK model
• Eternal traversable wormhole
• A semiclassical ramp in SYK and in gravity
• Scrambling and entanglement spreading in long-range spin chains
• Power-law out of time order correlation functions in the SYK model
• The statistical mechanics of near-extremal black holes
• Solvable Models of Quantum Black Holes: A Review on Jackiw-Teitelboim Gravity
• The Quantum Gravity Dynamics of Near Extremal Black Holes
• Notes on the complex Sachdev-Ye-Kitaev model
• The Bulk Dual of SYK: Cubic Couplings
• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• Onset of Random Matrix Behavior in Scrambling Systems
• Towards a full solution of the large N double-scaled SYK model
• An introduction to the SYK model
• Supersymmetric SYK model and random matrix theory
• Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
• Scrambling the spectral form factor: unitarity constraints and exact results
• The Schwarzian Theory - Origins
• The bulk Hilbert space of double scaled SYK
• Statistical mechanics of a two-dimensional black hole
• Low-dimensional de Sitter quantum gravity
• Many-Body Chaos in the Sachdev-Ye-Kitaev Model
• Cooper pairing of incoherent electrons: an electron-phonon version of the Sachdev-Ye-Kitaev model
• The Schwarzian Theory - A Wilson Line Perspective
• A Supersymmetric SYK-like Tensor Model
• Chord diagrams, exact correlators in spin glasses and black hole bulk reconstruction
• Quantum Simulation of Hyperbolic Space with Circuit Quantum Electrodynamics: From Graphs to Geometry
• Large $N$ theory of critical Fermi surfaces
• A universal Schwarzian sector in two-dimensional conformal field theories
• An exact quantization of Jackiw-Teitelboim gravity
• Quantum chaos transition in a two-site SYK model dual to an eternal traversable wormhole
• Liouville quantum gravity -- holography, JT and matrices
• Shockwave S-matrix from Schwarzian Quantum Mechanics
• Eigenstate thermalization in the Sachdev-Ye-Kitaev model
• Defects in Jackiw-Teitelboim Quantum Gravity
• Free Energy from Replica Wormholes
• Quantum ergodicity in the SYK model
• Hamiltonian deformations in quantum mechanics, $T\bar{T}$, and SYK
• Competition between Chaotic and Non-Chaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model
• Quantum chaos in the Brownian SYK model with large finite $N$: OTOCs and tripartite information
• Symmetries Near the Horizon
• Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Dispersive SYK model: band structure and quantum chaos
• Jackiw-Teitelboim Gravity and Rotating Black Holes
• De Sitter Horizons & Holographic Liquids
• Menagerie of AdS${}_2$ boundary conditions
• Tunable Quantum Chaos in the Sachdev-Ye-Kitaev Model Coupled to a Thermal Bath
• Flat space holography and complex SYK
• Correlators in tensor models from character calculus
• Large $N$ theory of critical Fermi surfaces II: conductivity
• Ward identities and combinatorics of rainbow tensor models
• Lindbladian dissipation of strongly-correlated quantum matter
• Euclidean wormhole in the SYK model
• Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev Model
• Eigenbranes in Jackiw-Teitelboim gravity
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• On the Chaos Bound in Rotating Black Holes
• Universal level statistics of the out-of-time-ordered operator
• Optical lattice platform for the SYK model
• SYK non Fermi Liquid Correlations in Nanoscopic Quantum Transport
• Entanglement Entropy, OTOC and Bootstrap in 2D CFTs from Regge and Light Cone Limits of Multi-point Conformal Block
• Towards a bulk description of higher spin SYK
• Evaporation dynamics of the Sachdev-Ye-Kitaev model
• Does the SYK model have a spin glass phase?
• Looking at supersymmetric black holes for a very long time
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Vector models and generalized SYK models
• Clocks and Rods in Jackiw-Teitelboim Quantum Gravity
• The double scaled limit of Super--Symmetric SYK models
• Periodically Driven Sachdev-Ye-Kitaev Models
• Exact moments of the Sachdev-Ye-Kitaev model up to order $1/N^2$
• Pedagogical introduction to SYK model and 2D Dilaton Gravity
• Thermoelectric power of Sachdev-Ye-Kitaev islands: Probing Bekenstein-Hawking entropy in quantum matter experiments
• Dynamical actions and q-representation theory for double-scaled SYK
• Holography for people with no time
• Supersymmetric SYK models
• Towards Black Hole Evaporation in Jackiw-Teitelboim Gravity
• Cut and join operator ring in Aristotelian tensor model
• Disorder in the Sachdev-Yee-Kitaev Model
• From Quantum Groups to Liouville and Dilaton Quantum Gravity
• Periodic Table of SYK and supersymmetric SYK
• Quantum criticality of granular SYK matter
• Chaos in a classical limit of the Sachdev-Ye-Kitaev model
• Excitation spectra of quantum matter without quasiparticles I: Sachdev-Ye-Kitaev models
• Comments on the Random Thirring Model
• Quench, thermalization and residual entropy across a non-Fermi liquid to Fermi liquid transition
• Low-rank Sachdev-Ye-Kitaev models
• Spectral Fluctuations in the Sachdev-Ye-Kitaev Model
• Nonperturbative effects and resurgence in JT gravity at finite cutoff
• Low-high voltage duality in tunneling spectroscopy of the Sachdev-Ye-Kitaev model
• Quantum critical Eliashberg theory, the SYK superconductor and their holographic duals
• Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model
• Supersymmetric SYK Model with Global Symmetry
• SYK model with quadratic perturbations: the route to a non-Fermi-liquid
• Two dimensional Nearly de Sitter gravity
• Topological Sachdev-Ye-Kitaev Model
• The Exact Solution of the Schwarzian Theory
• Quenched vs Annealed: Glassiness from SK to SYK
• Replica-nondiagonal solutions in the SYK model
• Supergroup Structure of Jackiw-Teitelboim Supergravity
• Complex Sachdev-Ye-Kitaev model in the double scaling limit
• Linear in temperature resistivity in the limit of zero temperature from the time reparameterization soft mode
• Thickening and sickening the SYK model
• SYK Superconductivity: Quantum Kuramoto and Generalized Richardson Models
• From Kronecker to tableau pseudo-characters in tensor models
• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
• Unruh detectors and quantum chaos in JT gravity
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• Chaos and random matrices in supersymmetric SYK
• Perturbed Sachdev-Ye-Kitaev model: a polaron in the hyperbolic plane
• Rotating Black Holes in AdS, Extremality and Chaos
• Superconductivity of incoherent electrons in Yukawa-SYK model
• The tenfold way and many-body zero modes in the Sachdev-Ye-Kitaev model
• Many-Body Localization in a finite-range Sachdev-Ye-Kitaev model
• Non-local reparametrization action in coupled Sachdev-Ye-Kitaev models
• JT Gravity Limit of Liouville CFT and Matrix Model
• Conformality of $1/N$ corrections in SYK-like models
• On the replica structure of Sachdev-Ye-Kitaev model
• Degenerate operators in JT and Liouville (super)gravity
• Half-wormholes in nearly AdS${}_2$ holography
• Jackiw-Teitelboim Model Coupled to Conformal Matter in the Semi-Classical Limit
• A Note on Sachdev-Ye-Kitaev Like Model without Random Coupling
• Extended Eigenstate Thermalization and the role of FZZT branes in the Schwarzian theory
• On 2D gauge theories in Jackiw-Teitelboim gravity
• Chaos on the hypercube
• Phase diagram of a two-site coupled complex Sachdev-Ye-Kitaev model
• Eigenstate Thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach
• Large $N$ expansion of the moments and free energy of Sachdev-Ye-Kitaev model, and the enumeration of intersection graphs
• Size of bulk fermions in the SYK model
• Bound on Lyapunov exponent in Einstein-Maxwell-Dilaton-Axion black holes
• Correlation functions in the Schwarzian theory
• Jackiw-Teitelboim quantum gravity with defects and the Aharonov-Bohm effect
• Chiral Algebras of Two-Dimensional SYK Models
• Notes on the SYK model in real time
• Chaos in Three-dimensional Higher Spin Gravity
• Decoherence and Microscopic Diffusion at SYK
• Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models
• Tearing down spacetime with quantum disentanglement
• Soft modes in $\mathcal{N}=2$ SYK model
• Slow scrambling in sonic black holes
• Schwarzian correction to quantum correlation in SYK model
• Exact Solutions of (deformed) Jackiw-Teitelboim Gravity
• Schwarzian functional integrals calculus
• Quantum thermal transport in the charged Sachdev-Ye-Kitaev model: Thermoelectric Coulomb blockade
• One-dimensional Quantum Gravity and the Schwarzian theory
• Unusual view of the Schwarzian theory
• On 1D, N = 4 Supersymmetric SYK-Type Models (I)
• Phase transitions for deformations of JT supergravity and matrix models
• Gapless odd-frequency superconductivity induced by the Sachdev-Ye-Kitaev model
• Quantum Correction to Chaos in Schwarzian Theory
• One SYK SET
• On Quantum Complexity
• Ensemble averages, Poisson processes and Microstates
• Multi-trace Correlators in the SYK Model and Non-geometric Wormholes
• Quantum discontinuity fixed point and renormalization group flow of the SYK model
• On 1/N diagrammatics in the SYK model beyond the conformal limit
• Operator Product Expansion in Liouville Field Theory and Seiberg type transitions in log-correlated Random Energy Models
• Conformal Bootstrap in dS/CFT and Topological Quantum Gravity
• Quantization of Jackiw-Teitelboim gravity with a massless scalar
• JT gravity at finite cutoff
• Les Houches lectures on two-dimensional gravity and holography
• True SYK or (con)sequences
• Steady state of the KPZ equation on an interval and Liouville quantum mechanics
• Simple rules of functional integration in the Schwarzian theory: SYK correlators
• Hamiltonian Dynamics of a Sum of Interacting Random Matrices
• Factorizing Wormholes in a Partially Disorder-Averaged SYK Model
• Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics
• Approximate Quantum Codes From Long Wormholes
• Phase space holography with no strings attached
• Defect conformal field theory from Sachdev-Ye-Kitaev interactions
• SYK does not Transit Gloria Mundi just yet
• Field theory for monitored Brownian SYK clusters
• A Microscopic Model of Black Hole Evaporation in Two Dimensions
• JT gravity and near-extremal thermodynamics for Kerr black holes in $Ad{S}_{4,5}$ for rotating perturbations
• Retrieving black hole information from the main Lorentzian saddle point
• Boundary correlators and the Schwarzian mode
• Gas of baby universes in JT gravity and matrix models
• Sixfold Way of Traversable Wormholes in the Sachdev-Ye-Kitaev Model
• Quantum quench, large N, and symmetry restoration
• Non-equilibrium Sachdev-Ye-Kitaev model with quadratic perturbation
• High-frequency transport and zero-sound in an array of SYK quantum dots
• Hierarchical analytical approach to universal spectral correlations in Brownian Quantum Chaos
• Attenuating Dynamics of Strongly Interacting Fermionic Superfluids in SYK Solvable Models
• Quenches and (Pre)Thermalisation in a mixed Sachdev-Ye-Kitaev Model
• The chiral SYK model in three-dimensional holography
• Matter Coupling of Dirac Matter in the Context of the SYK Model: Non-Gaussian Random Couplings and Bulk Mass Deformations
• The butterfly effect in a Sachdev-Ye-Kitaev quantum dot system
• An Approach to Quantum 2D Gravity
• Replica Symmetry Breaking in Random Non-Hermitian Systems
• Functional integration over the factor-space $Dif{f}_{+}^1(S^1)/SL(2,\text{R})$
• Quantum chaos in 2D gravity
• Schur Connections: Chord Counting, Line Operators, and Indices
• Noise signatures of a charged Sachdev-Ye-Kitaev dot in mesoscopic transport
• Realizing Unitary $k$-designs with a Single Quench
• Integrability and Spectral Form Factor in Chern-Simons Formulation
• On the nonclassicality in quantum JT gravity
• Pseudo-hermitian Chebyshev differential matrix and non-Hermitian Liouville quantum mechanics