Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems

Abstract

We show that the out-of-time-order correlation (OTOC) $⟨W(t{)}^{†}V(0{)}^{†}W(t)V(0)⟩$ in many-body localized (MBL) and marginal MBL systems can be efficiently calculated by the spectrum bifurcation renormalization group (SBRG). We find that in marginal MBL systems, the scrambling time $t_{\text{scr}}$ follows a stretched exponential scaling with the distance $d_{WV}$ between the operators $W$ and $V$: $t_{\text{scr}}\sim \exp (\sqrt{d_{WV}/l_0})$, which demonstrates Sinai diffusion of quantum information and the enhanced scrambling by the quantum criticality in non-chaotic systems.

6 pages, 4 figures

References in corpus (21)

• Many body localization and thermalization in quantum statistical mechanics
• Comments on the Sachdev-Ye-Kitaev model
• Black holes as mirrors: quantum information in random subsystems
• Many body localization in Heisenberg XXZ magnet in a random field
• Phenomenology of fully many-body-localized systems
• Theory of universal incoherent metallic transport
• Constructing local integrals of motion in the many-body localized phase
• Slow scrambling in disordered quantum systems
• Out-of-time-ordered correlators in many-body localized systems
• Numerical study of fermion and boson models with infinite-range random interactions
• Out-of-time-order correlations in many-body localized and thermal phases
• Measurement of many-body chaos using a quantum clock
• Universal Diffusion in Incoherent Black Holes
• Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
• Entanglement spreading in a many-body localized system
• Quantum criticality of hot random spin chains
• Marginal Anderson localization and many body delocalization
• Universal Logarithmic Scrambling in Many Body Localization
• Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space
• Disordered XYZ Spin Chain Simulations using the Spectrum Bifurcation Renormalization Group
• Sinai Diffusion at Quasi-1D Topological Phase Transitions

Cited by in corpus (40)

• Out-of-time-ordered correlators in quantum Ising chain
• Information propagation in isolated quantum systems
• Experimental Observation of Equilibrium and Dynamical Quantum Phase Transitions via Out-of-Time-Ordered Correlators
• Dynamics of entanglement and transport in 1D systems with quenched randomness
• Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial
• Gauging classical and quantum integrability through out-of-time ordered correlators
• Emergent prethermalization signatures in out-of-time ordered correlations
• Information scrambling in chaotic systems with dissipation
• Scrambling in strongly chaotic weakly coupled bipartite systems: Universality beyond the Ehrenfest time-scale
• Out of Time Ordered Correlators and Entanglement Growth in the Random Field XX Spin Chain
• Classification of out-of-time-order correlators
• Entanglement Features of Random Hamiltonian Dynamics
• Out-of-time-order correlations and Floquet dynamical quantum phase transition
• Topological and symmetry-enriched random quantum critical points
• Typical growth behavior of the out-of-time-ordered commutator in many-body localized systems
• Out-of-time-ordered correlators in short-range and long-range hard-core boson models and in the Luttinger-liquid model
• Signatures of quantum chaos transition in short spin chains
• Artificial Neural Network Based Computation for Out-of-Time-Ordered Correlators
• Dynamical Scaling Laws of Out-of-Time-Ordered Correlators
• Out-of-Time-Ordered Correlators in $(T^2{)}^n/{\mathbb{Z}}_n$
• Out-of-time-ordered correlation functions in open systems: A Feynman-Vernon influence functional approach
• Signatures of quantum chaos in an out-of-time-order tensor
• Transport, correlations, and chaos in a classical disordered anharmonic chain
• Entanglement dynamics in critical random quantum Ising chain with perturbations
• Out-of-Time-Order Correlators in One-Dimensional XY model
• Universal properties of many-body quantum chaos at Gross-Neveu criticality
• Estimating ergodization time of a chaotic many-particle system from a time reversal of equilibrium noise
• Asymmetric butterfly velocities in 2-local Hamiltonians
• Quantum Lyapunov exponent in dissipative systems
• Thermalization propagation front and robustness against avalanches in localized systems
• Information Trapping by Topologically Protected Edge States: Scrambling and the Butterfly Velocity
• Relevant OTOC operators: footprints of the classical dynamics
• Adding boundary terms to Anderson localized Hamiltonians leads to unbounded growth of entanglement
• Directional scrambling of quantum information in helical multiferroics
• Information scrambling and entanglement dynamics in Floquet Time Crystals
• Learning out-of-time-ordered correlators with classical kernel methods
• Scrambling dynamics across a thermalization-localization quantum phase transition
• Symmetry resolved out-of-time-order correlators of Heisenberg spin chains using projected matrix product operators
• Entanglement Growth from Entangled States: A Unified Perspective on Entanglement Generation and Transport
• Krylov complexity of many-body localization: Operator localization in Krylov basis