Solvable model for a dynamical quantum phase transition from fast to slow scrambling

Abstract

We propose an extension of the Sachdev-Ye-Kitaev (SYK) model that exhibits a quantum phase transition from the previously identified non-Fermi liquid fixed point to a Fermi liquid like state, while still allowing an exact solution in a suitable large $N$ limit. The extended model involves coupling the interacting $N$-site SYK model to a new set of $pN$ peripheral sites with only quadratic hopping terms between them. The conformal fixed point of the SYK model remains a stable low energy phase below a critical ratio of peripheral sites $p<p_c(n)$ that depends on the fermion filling $n$. The scrambling dynamics throughout the non-Fermi liquid phase is characterized by a universal Lyapunov exponent ${\lambda }_L\to 2\pi T$ in the low temperature limit, however the temperature scale marking the crossover to the conformal regime vanishes continuously at the critical point $p_c$. The residual entropy at $T\to 0$, non zero in the NFL, also vanishes continuously at the critical point. For $p>p_c$ the quadratic sites effectively screen the SYK dynamics, leading to a quadratic fixed point in the low temperature and frequency limit. The interactions have a perturbative effect in this regime leading to scrambling with Lyapunov exponent ${\lambda }_L\propto T^2$.

20 pages, 12 figures, added the calculation for Lyapunov exponent away from the particle-hole symmetric situation

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Cited by in corpus (182)

• Operator Spreading in Random Unitary Circuits
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• Power-law out of time order correlation functions in the SYK model
• More on Supersymmetric and 2d Analogs of the SYK Model
• Quantum information scrambling in a trapped-ion quantum simulator with tunable range interactions
• The Bulk Dual of SYK: Cubic Couplings
• Analytical Spectral Density of the Sachdev-Ye-Kitaev Model at finite N
• An introduction to the SYK model
• Quantum chaos on a critical Fermi surface
• Experimental Observation of Equilibrium and Dynamical Quantum Phase Transitions via Out-of-Time-Ordered Correlators
• Onset of many-body chaos in the $O(N)$ model
• Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
• Dynamics of entanglement and transport in 1D systems with quenched randomness
• Solvable Sachdev-Ye-Kitaev models in higher dimensions: from diffusion to many-body localization
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• A Supersymmetric SYK-like Tensor Model
• Approximating the Sachdev-Ye-Kitaev model with Majorana wires
• Quantum holography in a graphene flake with an irregular boundary
• Instability of the non-Fermi liquid state of the Sachdev-Ye-Kitaev Model
• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Out-of-Time-Ordered-Correlator Quasiprobabilities Robustly Witness Scrambling
• Probing scrambling using statistical correlations between randomized measurements
• 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
• Quantum Entanglement of the Sachdev-Ye-Kitaev Models
• Competition between Chaotic and Non-Chaotic Phases in a Quadratically Coupled Sachdev-Ye-Kitaev Model
• Many-body localization, symmetry, and topology
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• 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
• Many-Body Localization: Stability and Instability
• An exponential ramp in the quadratic Sachdev-Ye-Kitaev model
• Random Matrices and Holographic Tensor Models
• Light-cone spreading of perturbations and the butterfly effect in a classical spin chain
• Dynamics and Transport at the Threshold of Many-Body Localization
• Scrambling and Complexity in Phase Space
• SYK Models and SYK-like Tensor Models with Global Symmetry
• Correlators in the $\mathcal{N}=2$ Supersymmetric SYK Model
• Revival dynamics in a traversable wormhole
• Absence of fast scrambling in thermodynamically stable long-range interacting systems
• Quantum Simulation of the Non-Fermi-Liquid State of Sachdev-Ye-Kitaev Model
• A model for continuous thermal Metal to Insulator Transition
• Strange metal from local quantum chaos
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• Evaporation dynamics of the Sachdev-Ye-Kitaev model
• Higher-dimensional SYK Non-Fermi Liquids at Lifshitz transitions
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• Symmetry Breaking in Coupled SYK or Tensor Models
• Nonlinear sigma model approach to many-body quantum chaos: Regularized and unregularized out-of-time-ordered correlators
• SYK-like Tensor Models on the Lattice
• SYK Model, Chaos and Conserved Charge
• A cavity-QED simulator of slow and fast scrambling
• Vector models and generalized SYK models
• Dynamical phase transitions in sampling complexity
• Periodically Driven Sachdev-Ye-Kitaev Models
• Bound on the exponential growth rate of out-of-time-ordered correlators
• Supersymmetric SYK Model: Bi-local Collective Superfield/Supermatrix Formulation
• Interacting Majorana Fermions
• Diffusion in higher dimensional SYK model with complex fermions
• Contrasting SYK-like Models
• Phases Of Melonic Quantum Mechanics
• Diagnosing quantum chaos in many-body systems using entanglement as a resource
• Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models
• Eigenstate Thermalization Scaling in Majorana Clusters: from Chaotic to Integrable Sachdev-Ye-Kitaev Models
• Scrambling in the Dicke model
• Universal subdiffusion in strongly tilted many-body systems
• Traversable wormhole and Hawking-Page transition in coupled complex SYK models
• Comments on the Random Thirring Model
• Quench, thermalization and residual entropy across a non-Fermi liquid to Fermi liquid transition
• Towards a Finite-$N$ Hologram
• Strengthening weak measurements of qubit out-of-time-order correlators
• Charge transport in graphene-based mesoscopic realizations of Sachdev-Ye-Kitaev models
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• Many-body Chaos in Thermalised Fluids
• Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model
• Supersymmetric SYK Model with Global Symmetry
• Typical growth behavior of the out-of-time-ordered commutator in many-body localized systems
• Marginal Deformations and Rotating Horizons
• SYK model with quadratic perturbations: the route to a non-Fermi-liquid
• Topological Sachdev-Ye-Kitaev Model
• Classical Glasses, Black Holes, and Strange Quantum Liquids
• Strongly measuring qubit quasiprobabilities behind out-of-time-ordered correlators
• Thickening and sickening the SYK model
• Family of Sachdev-Ye-Kitaev models motivated by experimental considerations
• SYK Superconductivity: Quantum Kuramoto and Generalized Richardson Models
• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
• Entanglement Entropy and its Quench Dynamics for Pure States of the Sachdev-Ye-Kitaev model
• $\mathcal{N}=(0,2)$ SYK, Chaos and Higher-Spins
• A candidate Theory for the "Strange Metal" phase at Finite Energy Window
• Perturbed Sachdev-Ye-Kitaev model: a polaron in the hyperbolic plane
• Many-Body Localization in a finite-range Sachdev-Ye-Kitaev model
• Tunneling through an Eternal Traversable Wormhole
• Conformality of $1/N$ corrections in SYK-like models
• Scrambling versus relaxation in Fermi and non-Fermi liquids
• On the replica structure of Sachdev-Ye-Kitaev model
• Strange Half Metals and Mott Insulators in SYK Models
• Traversable wormhole in coupled SYK models with imbalanced interactions
• Dynamical Scaling Laws of Out-of-Time-Ordered Correlators
• Abelian Tensor Models on the Lattice
• Entanglement formation in continuous-variable random quantum networks
• Thermalization of non-Fermi-liquid electron-phonon systems: Hydrodynamic relaxation of the Yukawa-Sachdev-Ye-Kitaev model
• Quantum to classical crossover in many-body chaos and scrambling from relaxation in a glass
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• Information scrambling in a collision model
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• Variational wavefunctions for Sachdev-Ye-Kitaev models
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• Page Curve from Non-Markovianity
• Comment on "Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model"
• Supersymmetry method for interacting chaotic and disordered systems: the SYK model
• Global phase diagram of the one-dimensional Sachdev-Ye-Kitaev model at finite $N$
• Magneto-Thermoelectric Transport in Graphene Quantum Dot with Strong Correlations
• Quantum information scrambling in non-Markovian open quantum systems
• Disconnecting a Traversable Wormhole: Universal Quench Dynamics in Random Spin Models
• Slow scrambling in sonic black holes
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• Gapless odd-frequency superconductivity induced by the Sachdev-Ye-Kitaev model
• One SYK SET
• On 1D, N = 4 Supersymmetric SYK-Type Models (I)
• Complete Solution of a Gauged Tensor Model
• An SYK-inspired model with density-density interactions: spectral & wave function statistics, Green's function and phase diagram
• Violation and Revival of Kramers' Degeneracy in Open Quantum Systems
• Isolated zeros in the spectral function as signature of a quantum continuum
• Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
• Planckian superconductor
• Thermalization of Randomly Coupled SYK Models
• Transport properties of an interacting Majorana chain
• Operator Spreading in the Memory Matrix Formalism
• Sachdev-Ye-Kitaev type physics in the strained Kitaev honeycomb model
• Slow scrambling and hidden integrability in a random rotor model
• The tenfold way redux: Fermionic systems with $N$-body interactions
• Quantum Chaos of the Bose-Fermi Kondo model at the intermediate temperature
• Quantum discontinuity fixed point and renormalization group flow of the SYK model
• Towards quantum simulation of Sachdev-Ye-Kitaev model
• Bulk Reconstruction from Generalized Free Fields
• Many-body chaos in the antiferromagnetic quantum critical metal
• Optimally scrambling chiral spin-chain with effective black hole geometry
• Mimicking black hole event horizons in atomic and solid-state systems
• Quantum Chaos, Thermodynamics and Black Hole Microstates in the mass deformed SYK model
• Sign-Problem-Free Variant of Complex Sachdev-Ye-Kitaev Model
• Nematic phases and elastoresistivity from a multiorbital non-Fermi liquid
• SYK does not Transit Gloria Mundi just yet
• Dynamical quantum phase transitions from random matrix theory
• Floquet SYK wormholes
• Unambiguous measurement of information scrambling in a hierarchical star-topology system
• Exotic quantum statistics and thermodynamics from a number-conserving theory of Majorana fermions
• Super-maximal chaos and instability
• Non-Equilibrium Steady States and Quantum Chaos in a three-site Driven-Dissipative Bose-Hubbard Chains base on Self-Consistent Mean-Field Approach
• Quenches and (Pre)Thermalisation in a mixed Sachdev-Ye-Kitaev Model
• Many-body chaos and anomalous diffusion across thermal phase transitions in two dimensions
• Colliding poles with colliding nuclei
• Orbital selective order and ${\mathbb{Z}}_3$ Potts nematicity from a non-Fermi liquid
• Quantum Chaos of Unitary Fermi Gases in Strong Pairing Fluctuation Region
• Haar averaged moments of correlation functions and OTOCs in Floquet systems
• Revealing quantum operator scrambling via measuring Holevo information on digital quantum simulators
• Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
• Nematic order in topological SYK models
• The butterfly effect in a Sachdev-Ye-Kitaev quantum dot system
• Connecting Magic Dynamics in Thermofield Double States to Spectral Form Factors
• More on Complex Sachdev-Ye-Kitaev Eternal Wormholes
• Information scrambling and butterfly velocity in quantum spin glass chains
• Chaos-protected locality
• Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models
• Sachdev-Ye-Kitaev Model in a Quantum Glassy Landscape
• Hybrid Brownian SYK-Hubbard Model: from Spectral Function to Quantum Chaos
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems
• Wormholes and out-of-time ordered correlators in gauge/gravity duality
• A bipartite Sachdev-Ye-Kitaev model: Conformal limit and level statistics
• Phase Thermalization: from Fermi Liquid to Incoherent Metal