Disordered Lieb-Robinson bounds in one dimension

Abstract

By tightening the conventional Lieb-Robinson bounds to better handle systems which lack translation invariance, we determine the extent to which "weak links" suppress operator growth in disordered one-dimensional spin chains. In particular, we prove that ballistic growth is impossible when the distribution of coupling strengths $\mu (J)$ has a sufficiently heavy tail at small $J$, and identify the correct dynamical exponent to use instead. Furthermore, through a detailed analysis of the special case in which the couplings are genuinely random and independent, we find that the standard formulation of Lieb-Robinson bounds is insufficient to capture the complexity of the dynamics -- we must distinguish between bounds which hold for all sites of the chain and bounds which hold for a subsequence of sites, and we show by explicit example that these two can have dramatically different behaviors. All the same, our result for the dynamical exponent is tight, in that we prove by counterexample that there cannot exist any Lieb-Robinson bound with a smaller exponent. We close by discussing the implications of our results, both major and minor, for numerous applications ranging from quench dynamics to the structure of ground states.

arXiv comment23 pages, comments welcome

References in corpus (54)

• Many body localization and thermalization in quantum statistical mechanics
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Many-body localization, thermalization, and entanglement
• Phenomenology of fully many-body-localized systems
• A phenomenology of certain many-body-localized systems
• Lieb-Schultz-Mattis in Higher Dimensions
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• On Many-Body Localization for Quantum Spin Chains
• Spectral Gap and Exponential Decay of Correlations
• Floquet-Magnus Theory and Generic Transient Dynamics in Periodically Driven Many-Body Quantum Systems
• Exponentially slow heating in periodically driven many-body systems
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Quantum chaos challenges many-body localization
• Effective Hamiltonians, prethermalization and slow energy absorption in periodically driven many-body systems
• A strongly correlated metal built from Sachdev-Ye-Kitaev models
• Nearly-linear light cones in long-range interacting quantum systems
• Dynamical obstruction to localization in a disordered spin chain
• Distinguishing localization from chaos: challenges in finite-size systems
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Quantum Griffiths effects and smeared phase transitions in metals: theory and experiment
• Bounds on Information Propagation in Disordered Quantum Spin Chains
• Lieb-Robinson Bound and Locality for General Markovian Quantum Dynamics
• The Quantum Adiabatic Algorithm applied to random optimization problems: the quantum spin glass perspective
• Dynamics of entanglement and transport in 1D systems with quenched randomness
• Finite speed of quantum scrambling with long range interactions
• Strictly linear light cones in long-range interacting systems of arbitrary dimensions
• Quasi-Locality Bounds for Quantum Lattice Systems. Part I. Lieb-Robinson Bounds, Quasi-Local Maps, and Spectral Flow Automorphisms
• Hierarchy of linear light cones with long-range interactions
• The Lieb-Robinson light cone for power-law interactions
• Dynamical Localization in Disordered Quantum Spin Systems
• Fast State Transfer and Entanglement Renormalization Using Long-Range Interactions
• Separation of time-scales and reparametrization invariance for aging systems
• Fast scrambling on sparse graphs
• Information propagation for interacting particle systems
• SYK non Fermi Liquid Correlations in Nanoscopic Quantum Transport
• Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
• Information propagation through quantum chains with fluctuating disorder
• Dynamical phase transitions in sampling complexity
• Quantum algorithm for energy matching in hard optimization problems
• Efficiency versus Speed in Quantum Heat Engines: Rigorous Constraint from Lieb-Robinson Bound
• Lieb-Robinson bound and almost-linear light-cone in interacting boson systems
• Quantum criticality of granular SYK matter
• Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems
• A SWAP gate for qudits
• Lieb-Robinson bounds for commutator-bounded operators
• Finite speed of quantum information in models of interacting bosons at finite density
• Operator growth bounds from graph theory
• Locality and Heating in Periodically Driven, Power-law Interacting Systems
• Lieb-Robinson bounds for open quantum systems with long-ranged interactions
• Manifestations of dynamical localization in the disordered XXZ spin chain
• Generic Local Hamiltonians are Gapless
• On polynomial Lieb-Robinson bounds for the XY chain in a decaying random field
• Asymptotically Decreasing Lieb-Robinson Velocity for a Class of Dissipative Quantum Dynamics
• A Lieb-Robinson bound for quantum spin chains with strong on-site impurities

Cited by in corpus (6)

• Many-Body Localization in the Age of Classical Computing
• Speed limits and locality in many-body quantum dynamics
• The dynamical $\alpha$-Rényi entropies of local Hamiltonians grow at most linearly in time
• Sub-ballistic operator growth in spin chains with heavy-tailed random fields
• Lieb-Robinson correlation function for the quantum transverse field Ising model
• Lieb-Robinson bounds with exponential-in-volume tails