Lieb-Robinson Bounds on Entanglement Gaps from Symmetry-Protected Topology
arXiv:1904.12464
Abstract
A quantum quench is the simplest protocol to investigate nonequilibrium many-body quantum dynamics. Previous studies on the entanglement properties of quenched quantum many-body systems mainly focus on the growth of entanglement entropy. Several rigorous results and phenomenological guiding principles have been established, such as the no-faster-than-linear entanglement growth generated by generic local Hamiltonians and the peculiar logarithmic growth for many-body localized systems. However, little is known about the dynamical behavior of the full entanglement spectrum, which is a refined character closely related to the topological nature of the wave function. Here, we establish a rigorous and universal result for the entanglement spectra of 1D SPT systems evolving out of equilibrium. Our result is derived both for free-fermion SPT systems and interacting ones. For free-fermion systems with AZ symmetries, we prove that the single-particle entanglement gap after quenches obeys essentially the same Lieb-Robinson bound as that on the equal-time correlation, provided that there is no dynamical symmetry breaking. As a notable byproduct, we obtain a new type of Lieb-Robinson velocity which is related to the band dispersion with a complex wave number and reaches the minimum as the maximal (relative) group velocity. Within the framework of tensor networks, i.e., for SPT MPSs evolved by symmetric and trivial MPUs, we also identify a Lieb-Robinson bound on the many-body entanglement gap for general quenched interacting SPT systems. This result suggests high potential of tensor-network approaches for exploring rigorous results on long-time quantum dynamics. Influence of partial symmetry breaking, effects of disorder, and the relaxation property in the long-time limit are also discussed. Our work establishes a paradigm for exploring rigorous results of SPT systems out of equilibrium.
arXiv comment38 pages, 18 figures, 2 tables
References in corpus (127)
- Topological Insulators
- Topological insulators and superconductors
- Holographic Derivation of Entanglement Entropy from AdS/CFT
- Classification of topological insulators and superconductors in three spatial dimensions
- Maximally localized Wannier functions: Theory and applications
- Entanglement Entropy and Quantum Field Theory
- Thermalization and its mechanism for generic isolated quantum systems
- Area laws for the entanglement entropy - a review
- Classification of topological quantum matter with symmetries
- Nonequilibrium dynamics of closed interacting quantum systems
- Entanglement in quantum critical phenomena
- Probing many-body dynamics on a 51-atom quantum simulator
- Topological entanglement entropy
- Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
- Anderson Transitions
- Detecting topological order in a ground state wave function
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- The physics of exceptional points
- Symmetry and Topology in Non-Hermitian Physics
- Entanglement spectrum of a topological phase in one dimension
- Symmetry protected topological orders and the group cohomology of their symmetry group
- Time-dependence of correlation functions following a quantum quench
- Measuring entanglement entropy through the interference of quantum many-body twins
- Observation of a Discrete Time Crystal
- Quantum thermalization through entanglement in an isolated many-body system
- Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
- Calculation of reduced density matrices from correlation functions
- An Area Law for One Dimensional Quantum Systems
- Unbounded growth of entanglement in models of many-body localization
- Observation of discrete time-crystalline order in a disordered dipolar many-body system
- Classification of Gapped Symmetric Phases in 1D Spin Systems
- On the phase structure of driven quantum systems
- Zoo of quantum-topological phases of matter
- Observation of entanglement propagation in a quantum many-body system
- Light-cone-like spreading of correlations in a quantum many-body system
- Topological phases of fermions in one dimension
- Classifying quantum phases using Matrix Product States and PEPS
- Quantum entanglement in condensed matter systems
- Matrix product states represent ground states faithfully
- Operator Spreading in Random Unitary Circuits
- Area laws in quantum systems: mutual information and correlations
- Topological Origin of Zero-Energy Edge States in Particle-Hole Symmetric Systems
- Quantum Quench in the Transverse Field Ising Chain
- Lieb-Schultz-Mattis in Higher Dimensions
- Lieb-Robinson bounds and the generation of correlations and topological quantum order
- Quench dynamics and relaxation in isolated integrable quantum spin chains
- Quantum Quenches in Extended Systems
- Universal slow growth of entanglement in interacting strongly disordered systems
- Probing entanglement entropy via randomized measurements
- Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
- Inversion Symmetric Topological Insulators
- Many-body localization in periodically driven systems
- Probing entanglement in a many-body-localized system
- The Luttinger model following a sudden interaction switch-on
- Universal dynamics and renormalization in many body localized systems
- Area laws in a many-body localized state and its implications for topological order
- Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
- Violation of the entropic area law for Fermions
- Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
- Complete classification of 1D gapped quantum phases in interacting spin systems
- Exponential localization of Wannier functions in insulators
- Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
- Quasi-adiabatic Continuation of Quantum States: The Stability of Topological Ground State Degeneracy and Emergent Gauge Invariance
- Evolution of entanglement entropy following a quantum quench: Analytic results for the XY chain in a transverse magnetic field
- Entanglement spectrum of topological insulators and superconductors
- Entropy, entanglement, and area: analytical results for harmonic lattice systems
- Observation of a dynamical topological phase transition
- Matrix product operator representations
- Many-body localization in one dimension as a dynamical renormalization group fixed point
- Entanglement Entropy dynamics in Heisenberg chains
- Entanglement spectrum and boundary theories with projected entangled-pair states
- Out-of-Time-Order Correlation for Many-Body Localization
- String order and symmetries in quantum spin lattices
- Dynamical Topological Order Parameters far from Equilibrium
- Efficient tomography of a quantum many-body system
- Slow scrambling in disordered quantum systems
- Classification of Interacting Topological Floquet Phases in One Dimension
- New frontiers with quantum gases of polar molecules
- Out-of-time-ordered correlators in many-body localized systems
- Kitaev chains with long-range pairing
- Topological classification of dynamical phase transitions
- Entanglement growth in quench dynamics with variable range interactions
- Phase Structure of 1d Interacting Floquet Systems I: Abelian SPTs
- Nearly-linear light cones in long-range interacting quantum systems
- Dynamical preparation of Floquet Chern insulators
- Filling constraints for spin-orbit coupled insulators in symmorphic and non-symmorphic crystals
- The entanglement gap and a new principle of adiabatic continuity
- Renormalization group transformations on quantum states
- Topological Order and Absence of Band Insulators at Integer Filling in Non-Symmorphic Crystals
- Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
- The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
- Exponential Decay of Correlations Implies Area Law
- Uncover Topology by Quantum Quench Dynamics
- Quantum Quenches in Chern Insulators
- Measuring Topological Number of a Chern-Insulator from Quench Dynamics
- Bounds on Information Propagation in Disordered Quantum Spin Chains
- Floquet symmetry-protected topological phases in cold atomic systems
- An area law for entanglement from exponential decay of correlations
- Quantum Simulation and Spectroscopy of Entanglement Hamiltonians
- Matrix Product Unitaries: Structure, Symmetries, and Topological Invariants
- Persistence of locality in systems with power-law interactions
- Quantum quench in a p + i p superfluid: Winding numbers and topological states far from equilibrium
- Dynamical quantum phase transitions: Role of topological nodes in wavefunction overlaps
- Entanglement rates and area laws
- Dynamical topological invariant after a quantum quench
- Dynamical Buildup of a Quantized Hall Response from Non-Topological States
- Matrix Product Density Operators: Renormalization Fixed Points and Boundary Theories
- Entanglement entropy dynamics of disordered quantum spin chains
- Topological Entanglement-Spectrum Crossing in Quench Dynamics
- Persistent Hall response in a quantum quench
- Topological Marker Currents in Chern Insulators
- Dynamically enriched topological orders in driven two-dimensional systems
- Equilibration via Gaussification in fermionic lattice systems
- Localization with random time-periodic quantum circuits
- Classification of topological insulators and superconductors out of equilibrium
- Hall Response and Edge Current Dynamics in Chern Insulators out of Equilibrium
- Matrix Product Representation of Locality Preserving Unitaries
- Relaxation to gaussian and generalized Gibbs states in systems of particles with quadratic hamiltonians
- Classification of Matrix-Product Unitaries with Symmetries
- Spectral convergence bounds for classical and quantum Markov processes
- Spin Topological Field Theory and Fermionic Matrix Product States
- Topology and entanglement in quench dynamics
- Symmetry-protected entangling boundary zero modes in crystalline topological insulators
- Topological quantum quench dynamics carrying arbitrary Hopf and second-Chern numbers
- Signatures of information scrambling in the dynamics of the entanglement spectrum
- Approximating local properties by tensor network states with constant bond dimension