Finite-size prethermalization at the chaos-to-integrable crossover

Abstract

We investigate the infinite temperature dynamics of the complex Sachdev-Ye-Kitaev model (SYK${}_4$) complimented with a single particle hopping term (SYK${}_2$), leading to the chaos-to-integrable crossover of the many-body eigenstates. Due to the presence of the all-to-all connected SYK${}_2$ term, a non-equilibrium prethermal state emerges for a finite time window $t_{th}\propto 2^{a/{\lambda }^{2/5}}$ that scales with the relative interaction strength $\lambda$, between the SYK terms before eventually exhibiting thermalization for all $\lambda$. The scaling of the plateau with $\lambda$ is consistent with the many-body Fock space structure of the time-evolved wave function. In the integrable limit, the wavefunction in the Fock space has a stretched exponential dependence on distance. On the contrary, in the SYK${}_4$ limit, it is distributed equally over the Fock space points characterizing the ergodic phase at long times.

arXiv comment9 pages, 5 figures

References in corpus (71)

• Many body localization and thermalization in quantum statistical mechanics
• A bound on chaos
• Gapless Spin-Fluid Ground State in a Random Quantum Heisenberg Magnet
• Comments on the Sachdev-Ye-Kitaev model
• Many-body localization, thermalization, and entanglement
• The Kernel Polynomial Method
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Local conservation laws and the structure of the many-body localized states
• The Spectrum in the Sachdev-Ye-Kitaev Model
• Many-body localization: an introduction and selected topics
• The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
• Quantum chaos challenges many-body localization
• Theory of the many-body localization transition in one dimensional systems
• Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model
• Extended slow dynamical regime close to the many-body localization transition
• The Ergodic Side of the Many-Body Localization Transition
• Avalanches and many-body resonances in many-body localized systems
• Multifractal Scalings across the Many-Body Localization Transition
• Many-body localization characterized from a one-particle perspective
• Thouless time analysis of Anderson and many-body localization transitions
• Review: Local Integrals of Motion in Many-Body Localized systems
• Distinguishing localization from chaos: challenges in finite-size systems
• Ergodicity Breaking Transition in Finite Disordered Spin Chains
• Power-law out of time order correlation functions in the SYK model
• Evidence for unbounded growth of the number entropy in many-body localized phases
• Notes on the complex Sachdev-Ye-Kitaev model
• Can we study the many-body localisation transition?
• Dynamics at the Many-Body Localization Transition
• Anderson localization on random regular graphs
• Challenges to observation of many-body localization
• Polynomially filtered exact diagonalization approach to many-body localization
• Absence of true localization in many-body localized phases
• Thouless and relaxation time scales in many-body quantum systems
• Markovian baths and quantum avalanches
• Chaotic-Integrable Transition in the Sachdev-Ye-Kitaev Model
• Many-Body Delocalization in Strongly Disordered System with Long-Range Interactions: Finite Size Scaling
• Density propagator for many-body localization: finite size effects, transient subdiffusion, and exponential decay
• Rare thermal bubbles at the many-body localization transition from the Fock space point of view
• From Anderson localization on Random Regular Graphs to Many-Body localization
• Return probability for the Anderson model on the random regular graph
• Many-body localization transition with power-law interactions: Statistics of eigenstates
• Quantum ergodicity in the SYK model
• The Many-Body localization transition in the Hilbert space
• Critical behavior at the localization transition on random regular graphs
• Two critical localization lengths in the Anderson transition on random graphs
• Can many-body localization persist in the presence of long-range interactions or long-range hopping?
• Sub-diffusion in the Anderson model on random regular graph
• Slow dynamics and strong finite-size effects in many-body localization with random and quasi-periodic potential
• Eigenstate correlations around many-body localization transition
• Energy transport in the Anderson insulator
• Algebraic Many-Body Localization and its implications on information propagation
• Fock-space anatomy of eigenstates across the many-body localisation transition
• Density correlations and transport in models of many-body localization
• Self-consistent theory of many-body localisation in a quantum spin chain with long-range interactions
• Eigenstate Thermalization Scaling in Majorana Clusters: from Chaotic to Integrable Sachdev-Ye-Kitaev Models
• From operator statistics to wormholes
• A minimal model of many body localization
• Universal algebraic growth of entanglement entropy in many-body localized systems with power-law interactions
• Localisation on certain graphs with strongly correlated disorder
• Quantum criticality of granular SYK matter
• Unlimited growth of particle fluctuations in many-body localized phases
• Quench, thermalization and residual entropy across a non-Fermi liquid to Fermi liquid transition
• Many-body localization in large systems: Matrix-product-state approach
• SYK model with quadratic perturbations: the route to a non-Fermi-liquid
• Quantum ergodicity in the many-body localization problem
• Delayed Thermalization in Mass-Deformed SYK
• Quasi-Many-Body Localization of Interacting Fermions with Long-Range Couplings
• Multifractality and Fock-space localization in many-body localized states: one-particle density matrix perspective
• Probability transport on the Fock space of a disordered quantum spin chain
• An SYK-inspired model with density-density interactions: spectral & wave function statistics, Green's function and phase diagram

Cited by in corpus (5)

• Thermalization of a Closed Sachdev-Ye-Kitaev System in the Thermodynamic Limit
• Scaling of many-body localization transitions: Quantum dynamics in Fock space and real space
• Prethermalization for Deformed Wigner Matrices
• Universal non-equilibrium dynamics of pure states and density-dependent thermalization in Sachdev-Ye-Kitaev model
• From single-particle to many-body chaos in Yukawa--SYK: theory and a cavity-QED proposal