Typical growth behavior of the out-of-time-ordered commutator in many-body localized systems

Abstract

We investigate the typicality of the growth behavior of the out-of-time-ordered commutator (OTOC) in the many-body localized (MBL) quantum spin chains across random disorder realizations. In the MBL phase of the Heisenberg XXZ chain, we find that the estimate of the OTOC fluctuates significantly with the disorder realizations at the intermediate times of the main growth. Despite the consequent failure of the disorder average in the MBL phase, we argue that the characteristic behavior of the OTOC growth can still be identified by going through individual disorder realizations. We find that a power-law-type growth behavior appears typically after a disorder-dependent relaxation period, which is very close to the $t^2$ form derived in the effective Hamiltonian of a fully MBL system. The characteristic growth behavior observed at an individual disorder realization is robust in our tests with various state preparations and also verified in another MBL system of the random-transverse-field quantum Ising chain in a uniform longitudinal field.

References in corpus (68)

• Many body localization and thermalization in quantum statistical mechanics
• A bound on chaos
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Localization of interacting fermions at high temperature
• Comments on the Sachdev-Ye-Kitaev model
• Average Entropy of a Subsystem
• Black holes and the butterfly effect
• The many-body localization phase transition
• Black holes as mirrors: quantum information in random subsystems
• Fast Scramblers
• Many-body localization edge in the random-field Heisenberg chain
• Unbounded growth of entanglement in models of many-body localization
• Many body localization in Heisenberg XXZ magnet in a random field
• 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
• Localized shocks
• On Many-Body Localization for Quantum Spin Chains
• Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
• Black Holes and Random Matrices
• Universal dynamics and renormalization in many body localized systems
• Measuring the scrambling of quantum information
• Towards the fast scrambling conjecture
• Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
• Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models
• Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System
• Out-of-Time-Order Correlation for Many-Body Localization
• Ergodicity breaking in a model showing many-body localization
• Slow scrambling in disordered quantum systems
• Out-of-time-ordered correlators in many-body localized systems
• Scrambling and thermalization in a diffusive quantum many-body system
• Solvable model for a dynamical quantum phase transition from fast to slow scrambling
• Numerical study of fermion and boson models with infinite-range random interactions
• Many-body chaos at weak coupling
• Out-of-time-ordered correlators in quantum Ising chain
• Quantum quenches in the many-body localized phase
• Interferometric probes of many-body localization
• Black hole scrambling from hydrodynamics
• Information propagation in isolated quantum systems
• Out-of-time-order correlations in many-body localized and thermal phases
• Velocity-dependent Lyapunov exponents in many-body quantum, semi-classical, and classical chaos
• Weak Quantum Chaos
• Quantum chaos on a critical Fermi surface
• Measurement of many-body chaos using a quantum clock
• Jarzynski-like equality for the out-of-time-ordered correlator
• The quasiprobability behind the out-of-time-ordered correlator
• Chaos signatures in the short and long time behavior of the out-of-time ordered correlator
• Onset of many-body chaos in the $O(N)$ model
• Quantum butterfly effect in weakly interacting diffusive metals
• Out-of-Time-Order Correlation at a Quantum Phase Transition
• Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
• Entanglement spreading in a many-body localized system
• Quantum revivals and many-body localization
• Many-Body Quantum Interference and the Saturation of Out-of-Time-Order Correlators
• Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance and out-of-time-ordered correlator
• Out-of-time-ordered density correlators in Luttinger liquids
• Energy diffusion and the butterfly effect in inhomogeneous Sachdev-Ye-Kitaev chains
• Universal Logarithmic Scrambling in Many Body Localization
• Information scrambling in chaotic systems with dissipation
• Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems
• Exact out-of-time-ordered correlation functions for an interacting lattice fermion model
• Out-of-time-order correlators in finite open systems
• Out of Time Ordered Correlators and Entanglement Growth in the Random Field XX Spin Chain
• Slow growth of out-of-time-order correlators and entanglement in integrable disordered systems
• Scrambling in the Dicke model
• Strengthening weak measurements of qubit out-of-time-order correlators
• Loschmidt Echo in Many-Body Localized Phase
• Out-of-time-ordered measurements as a probe of quantum dynamics

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• Hamiltonian variational ansatz without barren plateaus
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions
• Logarithmic spreading of out-of-time-ordered correlators without many-body localization
• From ETH to algebraic relaxation of OTOCs in systems with conserved quantities
• Multifractality in quasienergy space of coherent states as a signature of quantum chaos
• Out-of-Time-Order Correlation as a Witness for Topological Phase Transitions
• Entanglement entropy and out-of-time-order correlator in the long-range Aubry-André-Harper model
• Signatures of quantum chaos in an out-of-time-order tensor
• Dynamics of spectral correlations in the entanglement Hamiltonian of the Aubry-André-Harper model
• Out of Time Order Correlations in the Quasi-Periodic Aubry-André model
• Information-Theoretic Memory Scaling in the Many-Body Localization Transition
• Slow relaxation of out-of-time-ordered correlators in interacting integrable and nonintegrable spin-1/2 XYZ chains
• Characteristic, dynamic, and near saturation regions of Out-of-time-order correlation in Floquet Ising models
• Scaling at the OTOC Wavefront: free versus chaotic models
• Effects of topological and non-topological edge states on information propagation and scrambling in a Floquet spin chain
• Hayden-Preskill Recovery in Hamiltonian Systems
• Signatures of the interplay between chaos and local criticality on the dynamics of scrambling in many-body systems
• Real-time dynamics of 1D and 2D bosonic quantum matter deep in the many-body localized phase
• Fast scrambling dynamics and many-body localization transition in an all-to-all disordered quantum spin model
• Relaxation exponents of OTOCs and overlap with local Hamiltonians
• Information scrambling and entanglement dynamics in Floquet Time Crystals
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
• Stabilizing confined quasiparticle dynamics in one-dimensional polar lattice gases
• Out-of-time-order correlators bridge classical transport and quantum dynamics
• Out-of-time-order correlators of nonlocal block-spin and random observables in integrable and nonintegrable spin chains