Late Time Quantum Chaos of pure states in the SYK model

Abstract

In this letter, we study the return amplitude, which is the overlap between the initial state and the time evolved state, in the Sachdev-Ye-Kitaev (SYK) model. Initial states are taken to be product states in a spin basis. We numerically study the return amplitude by exactly diagonalizing the Hamiltonian. We also derive the analytic expression for the return amplitude in random matrix theory. The SYK results agree with the random matrix expectation. We also study the time evolution under the different Hamiltonian that describes the traversable wormholes in projected black holes in the context of holography. The time evolution now depends on the choice of initial product states. The results are again explained by random matrix theory. In the symplectic ensemble cases, we observed an interesting pattern of the return amplitude where they show the second dip, ramp and plateau like behavior.

arXiv comment5 pages (+appendices), revtex. v2: comments and references are added

References in corpus (33)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Localization of interacting fermions at high temperature
• Comments on the Sachdev-Ye-Kitaev model
• Many-body localization edge in the random-field Heisenberg chain
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Topological phases of fermions in one dimension
• Integration with respect to the Haar measure on unitary, orthogonal and symplectic group
• Black Holes and Random Matrices
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Chaos, Complexity, and Random Matrices
• A semiclassical ramp in SYK and in gravity
• Sachdev-Ye-Kitaev Model and Thermalization on the Boundary of Many-Body Localized Fermionic Symmetry Protected Topological States
• Quantum quench of the Sachdev-Ye-Kitaev Model
• Thouless and relaxation time scales in many-body quantum systems
• Thermalization and Revivals after a Quantum Quench in Conformal Field Theory
• Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
• Scrambling the spectral form factor: unitarity constraints and exact results
• Anomalous Thouless energy and critical statistics on the metallic side of the many-body localization transition
• The spectral form factor is not self-averaging
• Complete random matrix classification of SYK models with $\mathcal{N}=0$, $1$ and $2$ supersymmetry
• Pure states in the SYK model and nearly-$Ad{S}_2$ gravity
• Work Statistics, Loschmidt Echo and Information Scrambling in Chaotic Quantum Systems
• Thouless time for mass-deformed SYK
• Echoes of chaos from string theory black holes
• Quantum Quenches and Thermalization in SYK models
• EPR Pairs, Local Projections and Quantum Teleportation in Holography
• Towards a Finite-$N$ Hologram
• On thermalization in the SYK and supersymmetric SYK models
• The Most Irrational Rational Theories
• Quantum Revivals in Conformal Field Theories in Higher Dimensions
• Revealing the interior of black holes out of equilibrium in the SYK model

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• Spectral form factor for free large $N$ gauge theory and strings
• Thermalization in different phases of charged SYK model
• Universal equilibration dynamics of the Sachdev-Ye-Kitaev model
• Dynamical Detection of Level Repulsion in the One-Particle Aubry-André Model
• Quantum Chaos, Thermodynamics and Black Hole Microstates in the mass deformed SYK model
• Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
• Euclidean-to-Lorentzian wormhole transition and gravitational symmetry breaking in the Sachdev-Ye-Kitaev model