Scrambling dynamics across a thermalization-localization quantum phase transition
arXiv:1807.06086 · doi:10.1103/PhysRevLett.123.165902
Abstract
We study quantum information scrambling, specifically the growth of Heisenberg operators, in large disordered spin chains using matrix product operator dynamics to scan across the thermalization-localization quantum phase transition. We observe ballistic operator growth for weak disorder, and a sharp transition to a phase with sub-ballistic operator spreading. The critical disorder strength for the ballistic to sub-ballistic transition is well below the many body localization phase transition, as determined from finite size scaling of energy eigenstate entanglement entropy in small chains. In contrast, we find that the transition from sub-ballistic to logarithmic behavior at the actual eigenstate localization transition is not resolved in our finite numerics. These data are discussed in the context of a universal form for the growing operator shape and substantiated with a simple phenomenological model of rare regions.
References in corpus (61)
- Many body localization and thermalization in quantum statistical mechanics
- Efficient classical simulation of slightly entangled quantum computations
- 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
- Efficient simulation of one-dimensional quantum many-body systems
- Black holes and the butterfly effect
- The many-body localization phase transition
- Real time evolution using the density matrix renormalization group
- Black holes as mirrors: quantum information in random subsystems
- Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
- 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
- Interacting electrons in disordered wires: Anderson localization and low-temperature transport
- 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
- Operator Spreading in Random Unitary Circuits
- Chaos in quantum channels
- On Many-Body Localization for Quantum Spin Chains
- Universal slow growth of entanglement in interacting strongly disordered systems
- Measuring out-of-time-order correlations and multiple quantum spectra in a trapped ion quantum magnet
- Many-body localization in a disordered quantum Ising chain
- Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
- Universal dynamics and renormalization in many body localized systems
- Area laws in a many-body localized state and its implications for topological order
- Measuring the scrambling of quantum information
- Localization protected quantum order
- Anomalous diffusion and Griffiths effects near the many-body localization transition
- Measuring out-of-time-order correlators on a nuclear magnetic resonance quantum simulator
- Theory of the many-body localization transition in one dimensional systems
- Recent progress in many-body localization
- Universal properties of many-body delocalization transitions
- Out-of-Time-Order Correlation for Many-Body Localization
- Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system
- Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
- Signatures of Many-Body Localization in a Controlled Open Quantum System
- Observation of Slow Dynamics near the Many-Body Localization Transition in One-Dimensional Quasiperiodic Systems
- Exploring Localization in Nuclear Spin Chains
- Slow scrambling in disordered quantum systems
- Out-of-time-ordered correlators in many-body localized systems
- Many-body Localization and Symmetry Protected Topological Order
- The Hilbert-glass transition: new universality of temperature-tuned many-body dynamical quantum criticality
- Rare region effects and dynamics near the many-body localization transition
- Critical Properties of the Many-Body Localization Transition
- Out-of-time-ordered correlators in quantum Ising chain
- 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
- Measurement of many-body chaos using a quantum clock
- Jarzynski-like equality for the out-of-time-ordered correlator
- Bounds on Information Propagation in Disordered Quantum Spin Chains
- Dynamics of entanglement and transport in 1D systems with quenched randomness
- Characterizing Many-Body Localization by Out-of-Time-Ordered Correlation
- Locality, Quantum Fluctuations, and Scrambling
- Spin transport of weakly disordered Heisenberg chain at infinite temperature
- Exploring quantum signatures of chaos on a Floquet synthetic lattice
- Out-of-Time-Order Correlation in Marginal Many-Body Localized Systems
- Asymmetry in energy versus spin transport in certain interacting, disordered systems