Out-of-equilibrium dynamics and thermalization of string order

Abstract

We investigate the equilibration dynamics of string order in one-dimensional quantum systems. After initializing a spin-1 chain in the Haldane phase, the time evolution of non-local correlations following a sudden quench is studied by means of matrix-product-state-based algorithms. Thermalization occurs only for scales up to a horizon growing at a well defined speed, due to the finite maximal velocity at which string correlations can propagate, related to a Lieb-Robinson bound. The persistence of string ordering at finite times is non-trivially related to symmetries of the quenched Hamiltonian. A qualitatively similar behavior is found for the string order of the Mott insulating phase in the Bose-Hubbard chain. This paves the way towards an experimental testing of our results in present cold-atom setups.

6 pages, 5 figures. Several changes; slightly extended version of PRB paper (non-symmetric Hamiltonians also addressed)

References in corpus (17)

• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Quantum Quench in the Transverse Field Ising Chain
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Interaction Quench in the Hubbard model
• Microscopic observation of magnon bound states and their dynamics
• Local emergence of thermal correlations in an isolated quantum many-body system
• Strong and weak thermalization of infinite non-integrable quantum systems
• Generalized Thermalization in an Integrable Lattice System
• String order and symmetries in quantum spin lattices
• Hidden order in 1D Bose insulators
• Rise and fall of hidden string order of lattice bosons
• Quantum Quenches, Thermalization and Many-Body Localization
• Phase diagram of the extended Bose Hubbard model
• Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined
• Non-local order parameters for the 1D Hubbard model
• Exact results on the quench dynamics of the entanglement entropy in the toric code

Cited by in corpus (19)

• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Quantum magnetism and topological ordering via enhanced Rydberg-dressing near Förster-resonances
• Topology of one dimensional quantum systems out of equilibrium
• Cooperative shielding in many-body systems with long-range interaction
• Shielding and localization in presence of long range hopping
• Dynamical topological quantum phase transitions in nonintegrable models
• Suppression of heating by long-range interactions in periodically driven spin chains
• Topological and dynamical properties of a generalized cluster model in one dimension
• Interaction-driven dynamical quantum phase transitions in a strongly correlated bosonic system
• Destruction of string order after a quantum quench
• Hidden Order in Quantum Many-body Dynamics of Driven-Dissipative Nonlinear Photonic Lattices
• Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles
• Interaction quench and thermalization in a one-dimensional topological Kondo insulator
• Spin fluctuations after quantum quenches in the S=1 Haldane chain: numerical validation of the semi-semiclassical theory
• Resilience of hidden order to symmetry-preserving disorder
• Topology in the space-time scaling limit of quantum dynamics
• Dynamics for the Haldane phase in the Bilinear-Biquadratic Model
• Emergence of topological states in relaxation dynamics of interacting bosons
• Dynamically generated quadrupole polarization using Floquet adiabatic evolution