Magnetization and energy dynamics in spin ladders: Evidence of diffusion in time, frequency, position, and momentum

Abstract

The dynamics of magnetization and energy densities are studied in the two-leg spin-1/2 ladder. Using an efficient pure-state approach based on the concept of typicality, we calculate spatio-temporal correlation functions for large systems with up to 40 lattice sites. In addition, two subsequent Fourier transforms from real to momentum space as well as from time to frequency domain yield the respective dynamic structure factors. Summarizing our main results, we unveil the existence of genuine diffusion both for spin and energy. In particular, this finding is based on four distinct signatures which can all be equally well detected: (i) Gaussian density profiles, (ii) time-independent diffusion coefficients, (iii) exponentially decaying density modes, and (iv) Lorentzian line shapes of the dynamic structure factor. The combination of (i) - (iv) provides a comprehensive picture of high-temperature dynamics in thisarchetypal nonintegrable quantum model.

arXiv comment12 pages, 11 figures

References in corpus (77)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Chaos and Quantum Thermalization
• Thermalization and its mechanism for generic isolated quantum systems
• Nonequilibrium dynamics of closed interacting quantum systems
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Quantum many-body systems out of equilibrium
• The Kernel Polynomial Method
• The foundations of statistical mechanics from entanglement: Individual states vs. averages
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Equilibration, thermalisation, and the emergence of statistical mechanics in closed quantum systems
• Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
• Operator Spreading in Random Unitary Circuits
• Canonical Typicality
• Generalized Gibbs ensemble in integrable lattice models
• Emergent hydrodynamics in integrable quantum systems out of equilibrium
• Operator hydrodynamics, OTOCs, and entanglement growth in systems without conservation laws
• Transport and conservation laws
• Thermodynamics of Spin S = 1/2 Antiferromagnetic Uniform and Alternating-Exchange Heisenberg Chains
• Operator spreading and the emergence of dissipative hydrodynamics under unitary evolution with conservation laws
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Hydrodynamic Diffusion in Integrable Systems
• Fractional spinon excitations in the quantum Heisenberg antiferromagnetic chain
• Ultracold atoms out of equilibrium
• Spin diffusion from an inhomogeneous quench in an integrable system
• Typicality for Generalized Microcanonical Ensembles
• Families of quasi-local conservation laws and quantum spin transport
• Canonical Thermal Pure Quantum State
• Magnon Heat Transport in (Sr,La)_14Cu_24O_41
• Conservation laws, integrability and transport in one-dimensional quantum systems
• Fast Algorithm for Finding the Eigenvalue Distribution of Very Large Matrices
• Zero-frequency transport properties of one dimensional spin-1/2 systems
• The thermal conductivity of the spin-1/2 XXZ chain at arbitrary temperature
• Multispinon continua at zero and finite temperature in a near-ideal Heisenberg chain
• Dynamical typicality of quantum expectation values
• An efficient scheme for numerical simulations of the spin-bath decoherence
• Real-time and real-space spin- and energy dynamics in one-dimensional spin-1/2 systems induced by local quantum quenches at finite temperatures
• Spin-current autocorrelations from single pure-state propagation
• Transport in Almost Integrable Models: Perturbed Heisenberg Chains
• A real-time study of diffusive and ballistic transport in spin-1/2 chains using the adaptive time-dependent density matrix renormalization group method
• Fourier's Law from Schroedinger Dynamics
• Nonequilibrium thermal transport and its relation to linear response
• 17O NMR study of q=0 spin excitations in a nearly ideal S=1/2 1D Heisenberg antiferromagnet, Sr2CuO3, up to 800 K
• Regression relation for pure quantum states and its implications for efficient computing
• Quantum correlations and entanglement in far-from-equilibrium spin systems
• Diffusion in deterministic interacting lattice systems
• Spin transport in the XXZ chain at finite temperature and momentum
• Diffusive high-temperature transport in the one-dimensional Hubbard model
• Fourier's Law in a Quantum Spin Chain and the Onset of Quantum Chaos
• Dynamic correlations of antiferromagnetic spin-1/2 XXZ chains at arbitrary temperature from complete diagonalization
• High temperature thermal conductivity of 2-leg spin-1/2 ladders
• Density dynamics in translationally invariant spin-1/2 chains at high temperatures: a current auto-correlation approach to finite time- and length-scales
• An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
• Coexistence of diffusive and ballistic transport in a simple spin ladder
• Real-time broadening of non-equilibrium density profiles and the role of the specific initial-state realization
• Algorithm for Linear Response Functions at Finite Temperatures: Application to ESR spectrum of s=1/2 Antiferromagnet Cu benzoate
• Dynamical typicality of isolated many-body quantum systems
• Spin and thermal conductivity of quantum spin ladders
• Scaling of diffusion constants in the spin-1/2 XX ladder
• Heat conductivity of the Heisenberg spin-1/2 ladder: From weak to strong breaking of integrability
• Density dynamics from current auto-correlations at finite time- and length-scales
• Energy diffusion in the ergodic phase of a many body localizable spin chain
• Proposal for measuring the finite-temperature Drude weight of integrable systems
• Magnetization transport in spin ladders and next-nearest-neighbor chains
• Real-Time Dynamics of Typical and Untypical States in Non-Integrable Systems
• Spin hydrodynamics in the S = 1/2 anisotropic Heisenberg chain
• Heat Transport in Spin Chains with Weak Spin-Phonon Coupling
• Local spin relaxation within the random Heisenberg chain
• Charge diffusion in the one-dimensional Hubbard model
• Thermal Transport in a one-dimensional Z${}_2$ Spin Liquid
• Low temperature ballistic spin transport in the S=1/2 antiferromagnetic Heisenberg chain compound SrCuO2
• Thermal transport in a spin-1/2 Heisenberg chain coupled to a (non) magnetic impurity
• Relation between far-from-equilibrium dynamics and equilibrium correlation functions for binary operators
• Energy spread and current-current correlation in quantum systems
• Dynamics in two-leg spin ladder with a four-spin cyclic interaction
• Stability of Quantum Dynamics under Constant Hamiltonian Perturbations
• Decoherence Entails Exponential Forgetting in Systems Complying with the Eigenstate Thermalization Hypothesis

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• Finite-temperature transport in one-dimensional quantum lattice models
• Superdiffusion in spin chains
• Evidence of Kardar-Parisi-Zhang scaling on a digital quantum simulator
• Simulating hydrodynamics on noisy intermediate-scale quantum devices with random circuits
• Random State Technology
• Selected applications of typicality to real-time dynamics of quantum many-body systems
• Transport and entanglement growth in long-range random Clifford circuits
• Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices
• Quantum dynamics in the interacting Fibonacci chain
• Exponential damping induced by random and realistic perturbations
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Magnetization dynamics in clean and disordered spin-1 XXZ chains
• Quantum simulation using noisy unitary circuits and measurements
• Non-ergodic one-magnon magnetization dynamics of the antiferromagnetic delta chain
• Relaxation of dynamically prepared out-of-equilibrium initial states within and beyond linear response theory
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Localisation and Sub-Diffusive Transport in Quantum Spin Chains With Dilute Disorder
• Transport and integrability-breaking in non-Hermitian many-body quantum systems
• Modeling the Impact of Hamiltonian Perturbations on Expectation Value Dynamics
• Hierarchy of timescales in a disordered spin-$1/2$ XX ladder