Quantum quenches in the anisotropic spin-1/2 Heisenberg chain: different approaches to many-body dynamics far from equilibrium

Abstract

Recent experimental achievements in controlling ultracold gases in optical lattices open a new perspective on quantum many-body physics. In these experimental setups it is possible to study coherent time evolution of isolated quantum systems. These dynamics reveal new physics beyond the low-energy properties usually relevant in solid-state many-body systems. In this paper we study the time evolution of antiferromagnetic order in the Heisenberg chain after a sudden change of the anisotropy parameter, using various numerical and analytical methods. As a generic result we find that the order parameter, which can show oscillatory or non-oscillatory dynamics, decays exponentially except for the effectively non-interacting case of the XX limit. For weakly ordered initial states we also find evidence for an algebraic correction to the exponential law. The study is based on numerical simulations using a numerical matrix product method for infinite system sizes (iMPS), for which we provide a detailed description and an error analysis. Additionally, we investigate in detail the exactly solvable XX limit. These results are compared to approximative analytical approaches including an effective description by the XZ-model as well as by mean-field, Luttinger-liquid and sine-Gordon theories. This reveals which aspects of non-equilibrium dynamics can as in equilibrium be described by low-energy theories and which are the novel phenomena specific to quantum quench dynamics. The relevance of the energetically high part of the spectrum is illustrated by means of a full numerical diagonalization of the Hamiltonian.

28 pages

References in corpus (58)

• Many-Body Physics with Ultracold Gases
• Thermalization and its mechanism for generic isolated quantum systems
• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Non-equilibrium coherence dynamics in one-dimensional Bose gases
• The ALPS project release 1.3: open source software for strongly correlated systems
• Time-resolved Observation and Control of Superexchange Interactions with Ultracold Atoms in Optical Lattices
• Quench dynamics and non equilibrium phase diagram of the Bose-Hubbard model
• Breakdown of thermalization in finite one-dimensional systems
• Foundation of Statistical Mechanics under experimentally realistic conditions
• The Luttinger model following a sudden interaction switch-on
• The iTEBD algorithm beyond unitary evolution
• Interaction Quench in the Hubbard model
• Dynamical phase transition in correlated fermionic lattice systems
• From density-matrix renormalization group to matrix product states
• Entanglement spectrum in one-dimensional systems
• Evidence for Superfluidity of Ultracold Fermions in an Optical Lattice
• The Statistics of the Work Done on a Quantum Critical System by Quenching a Control Parameter
• Spreading of correlations and entanglement after a quench in the one-dimensional Bose-Hubbard model
• Quench dynamics across quantum critical points
• Strongly correlated fermions after a quantum quench
• Supplementary Information to the paper ``Breakdown of the adiabatic limit in low dimensional gapless systems''
• Breakdown of the adiabatic limit in low dimensional gapless systems
• Universal theory of nonlinear Luttinger liquids
• Effective thermal dynamics following a quantum quench in a spin chain
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Quantum quenches and thermalization in one-dimensional fermionic systems
• Quantum transport through a Tonks-Girardeau gas
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• Matrix Product States for dynamical simulation of infinite chains
• Spectral functions in one-dimensional quantum systems at T>0
• Nonthermal steady states after an interaction quench in the Falicov-Kimball model
• Time-step targetting methods for real-time dynamics using DMRG
• Spectral Function for the S=1 Heisenberg Antiferromagetic Chain
• Coherent collisional spin dynamics in optical lattices
• Sublattice addressing and spin-dependent motion of atoms in a double-well lattice
• Time evolution algorithms for Matrix Product States and DMRG
• Relaxation of a one-dimensional Mott insulator after an interaction quench
• Exploring local quantum many-body relaxation by atoms in optical superlattices
• Non-equilibrium Gross-Pitaevskii dynamics of boson lattice models
• Time evolution of correlations in strongly interacting fermions after a quantum quench
• Quenches in quantum many-body systems: One-dimensional Bose-Hubbard model reexamined
• Quantum quenches from integrability: the fermionic pairing model
• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Correlations in an expanding gas of hard-core bosons
• Decoherence Dynamics in Low-Dimensional Cold Atom Interferometers
• Intrinsic dephasing in one dimensional ultracold atom interferometers
• Quantum Many-Body Dynamics of Coupled Double-Well Superlattices
• Orthogonality catastrophe and shock waves in a non-equilibrium Fermi gas
• Evolution of the macroscopically entangled states in optical lattices
• Adiabatic quenches through an extended quantum critical region
• Microscopic expression for the heat in the adiabatic basis
• Unitary perturbation theory approach to real-time evolution problems
• Magnetism, coherent many-particle dynamics, and relaxation with ultracold bosons in optical superlattices
• Ultracold gases far from equilibrium
• Form factors of boundary exponential operators in the sinh-Gordon model
• Ultracold atomic quantum gases far from equilibrium

Cited by in corpus (106)

• Quantum Quench in the Transverse Field Ising Chain
• Quench dynamics and relaxation in isolated integrable quantum spin chains
• Time evolution of local observables after quenching to an integrable model
• Quantum quenches in 1+1 dimensional conformal field theories
• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Quantum Quench in the Transverse Field Ising chain I: Time evolution of order parameter correlators
• Many-body localization in one dimension as a dynamical renormalization group fixed point
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• Reduced Density Matrix after a Quantum Quench
• Extended slow dynamical regime close to the many-body localization transition
• Algebraic versus exponential decoherence in dissipative many-particle systems
• Disentangling dynamical phase transitions from equilibrium phase transitions
• What is an integrable quench?
• Localization and Glassy Dynamics Of Many-Body Quantum Systems
• Relaxation after quantum quenches in the spin-1/2 Heisenberg XXZ chain
• Dynamical quantum phase transitions in systems with broken-symmetry phases
• Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
• Generalized Gibbs Ensembles for Quantum Field Theories
• Eigenstate thermalization hypothesis (ETH) and integrability in quantum spin chains
• Long time dynamics following a quench in an integrable quantum spin chain: local versus non-local operators and effective thermal behavior
• Quantum chaos and thermalization in gapped systems
• Quantum quench in the sine-Gordon model
• Stationary behaviour of observables after a quantum quench in the spin-1/2 Heisenberg XXZ chain
• On Conservation Laws, Relaxation and Pre-relaxation after a Quantum Quench
• Dynamics in the Ising field theory after a quantum quench
• Quantum Quenches in the Hubbard Model: Time Dependent Mean Field Theory and The Role of Quantum Fluctuations
• Quantum Quenches in an XXZ Spin Chain from a Spatially Inhomogeneous Initial State
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• Quantum relaxation after a quench in systems with boundaries
• Propagation front of correlations in an interacting Bose gas
• Generalized Gibbs Ensemble for Heisenberg Spin Chains
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Purification and many-body localization in cold atomic gases
• Quantum quenches as classical critical films
• Scaling approach to quantum non-equilibrium dynamics of many-body systems
• Quantum correlations and entanglement in far-from-equilibrium spin systems
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Many-body localization in infinite chains
• Simulating Quantum Materials with Digital Quantum Computers
• Coherent Interaction of a Single Fermion with a Small Bosonic Field
• An exact formalism for the quench dynamics of integrable models
• From the Quantum Transfer Matrix to the Quench Action: The Loschmidt echo in $XXZ$ Heisenberg spin chains
• Quench Dynamics of the Anisotropic Heisenberg Model
• Non-analytic behavior of the Loschmidt echo in XXZ spin chains: exact results
• Quantum quench within the gapless phase of the spin-1/2 Heisenberg XXZ spin-chain
• Nonequilibrium quantum dynamics of a charge carrier doped into a Mott insulator
• Locality and thermalization in closed quantum systems
• Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
• Quantum quenches and Generalized Gibbs Ensemble in a Bethe Ansatz solvable lattice model of interacting bosons
• Bound states and entanglement in the excited states of quantum spin chains
• Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains
• Dimensional Crossover Driven by an Electric Field
• How order melts after quantum quenches
• Nonlinear current response of an isolated system of interacting fermions
• Quasi locality of the GGE in interacting-to-free quenches in relativistic field theories
• The quench action approach in finite integrable spin chains
• Entanglement entropy of disordered quantum chains following a global quench
• The Hyperfine Molecular Hubbard Hamiltonian
• Symmetry-protected coherent relaxation of open quantum systems
• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
• Integrable Mott insulators driven by finite electric field
• Non-thermal melting of Neel order in the Hubbard model
• Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
• Many-body localization in the interpolating Aubry-André-Fibonacci model
• Quantum quench in 1D: Coherent inhomogeneity amplification and 'supersolitons'
• Real-time dynamics in a strongly interacting bosonic hopping model: Global quenches and mapping to the XX chain
• Quantum quench spectroscopy of a Luttinger liquid: Ultrarelativistic density wave dynamics due to fractionalization in an XXZ chain
• Non-equilibrium quantum dynamics after local quenches
• Interaction Quench in Nonequilibrium Luttinger Liquids
• Exact work statistics of quantum quenches in the anisotropic XY model
• Non-equilibrium Quantum Spin Dynamics from 2PI Functional Integral Techniques in the Schwinger Boson Representation
• Temporal decay of Neel order in the one-dimensional Fermi-Hubbard model
• Exact Real Time Dynamics of Quantum Spin Systems Using the Positive-P Representation
• Long time correlations of nonlinear Luttinger liquids
• Non-equilibrium and non-homogeneous phenomena around a first-order quantum phase transition
• Simulation of the Dynamics of Many-Body Quantum Spin Systems Using Phase-Space Techniques
• Long-range-ordered phase in a quantum Heisenberg chain with interactions beyond nearest neighbors
• Quenches and confinement in a Heisenberg-Ising spin ladder
• Dynamics of correlations in shallow optical lattices
• Time evolution during and after finite-time quantum quenches in Luttinger liquids
• Does a distinct quasi many-body localized phase exist? A numerical study of a translationally invariant system in the thermodynamic limit
• Propagation of a single hole defect in the one-dimensional Bose-Hubbard model
• Anomalous scaling at non-thermal fixed points of the sine-Gordon model
• Power-law decay of correlations after a global quench in the massive XXZ chain
• Exploring Dynamical Phase Transitions in the XY Chain through Linear Quench: Early and Long-term Perspectives
• Temporal relaxation of gapped many-body quantum systems
• Dynamics of rotated spin states and magnetic ordering with two-component bosonic atoms in optical lattices
• Dynamical relaxation behavior of extended XY chain with gapless phase following a quantum quench
• Quantum quench in 2D using the variational Baeriswyl wavefunction
• Loading and detecting a three-dimensional Fermi gas in one-dimensional optical superlattice
• On the Dynamics of XY Spin Chains with Impurities
• Relaxation dynamics of integrable field theories after a global quantum quench
• Dynamics and thermalization in correlated one-dimensional lattice systems
• Composable Programming of Hybrid Workflows for Quantum Simulation
• Optimal protocols for finite-duration quantum quenches in the Luttinger model
• Edge Spin fractionalization in one-dimensional spin-$S$ quantum antiferromagnets
• Finite-time quantum quenches in the XXZ Heisenberg chain
• Quench dynamics of two component dipolar fermions subject to a quasiperiodic potential
• Functionally independent conservations laws in a quantum integrable model
• Relaxation of antiferromagnetic order and growth of Rényi entropy in a generalized Heisenberg star
• Long-lived non-thermal states in pumped one-dimensional systems of hard-core bosons
• Relaxation dynamics in the alternating XY chain following a quantum quench
• Real-Time Dynamics of a Spin Chain with Dzyaloshinskii-Moriya Interactions: Spiral Formation and Quantum Spin Oscillations
• Entanglement in a fermionic spin chain containing a single mobile boson under decoherence
• Numerical Probe of Dynamical Properties of a Two-Dimensional Triangular Ising Lattice with Long-Range Interaction
• QuaSiMo: A Composable Library to Program Hybrid Workflows for Quantum Simulation