Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices

Abstract

We present a comprehensive comparison of spin and energy dynamics in quantum and classical spin models on different geometries, ranging from one-dimensional chains, over quasi-one-dimensional ladders, to two-dimensional square lattices. Focusing on dynamics at formally infinite temperature, we particularly consider the autocorrelation functions of local densities, where the time evolution is governed either by the linear Schrödinger equation in the quantum case, or the nonlinear Hamiltonian equations of motion in the case of classical mechanics. While, in full generality, a quantitative agreement between quantum and classical dynamics can therefore not be expected, our large-scale numerical results for spin-$1/2$ systems with up to $N=36$ lattice sites in fact defy this expectation. Specifically, we observe a remarkably good agreement for all geometries, which is best for the nonintegrable quantum models in quasi-one or two dimensions, but still satisfactory in the case of integrable chains, at least if transport properties are not dominated by the extensive number of conservation laws. Our findings indicate that classical or semi-classical simulations provide a meaningful strategy to analyze the dynamics of quantum many-body models, even in cases where the spin quantum number $S=1/2$ is small and far away from the classical limit $S\to \infty$.

11 pages, 7 figures

References in corpus (19)

• Many-Body Physics with Ultracold Gases
• The density-matrix renormalization group in the age of matrix product states
• Thermalization and its mechanism for generic isolated quantum systems
• Many body localization and thermalization in quantum statistical mechanics
• The Kernel Polynomial Method
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Ultracold atoms out of equilibrium
• Typicality for Generalized Microcanonical Ensembles
• Fermi, Pasta, Ulam and a mysterious lady
• Random phase vector for calculating the trace of a large matrix
• Domain wall dynamics in the Landau--Lifshitz magnet and the classical-quantum correspondence for spin transport
• Lectures on the Bethe Ansatz
• Largest Lyapunov exponents for lattices of interacting classical spins
• Equilibration and Thermalization of Classical Systems
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Effectiveness of classical spin simulations for describing NMR relaxation of quantum spins
• Quantum quench dynamics in the transverse-field Ising model: A numerical expansion in linked rectangular clusters
• Numerical linked cluster expansions for inhomogeneous systems
• Free induction decays in nuclear spin-1/2 lattices with small number of interacting neighbors: the cases of silicon and fluorapatite

Cited by in corpus (17)

• Multidimensional hyperspin machine
• Anomalous Dynamics and Equilibration in the Classical Heisenberg Chain
• Robustness of Kardar-Parisi-Zhang scaling in a classical integrable spin chain with broken integrability
• Diffusion constants from the recursion method
• Hydrodynamics in long-range interacting systems with center-of-mass conservation
• Quantum dynamics in one and two dimensions via recursion method
• Probing spin hydrodynamics on a superconducting quantum simulator
• Quantum-classical correspondence of strongly chaotic many-body spin models
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
• Quantifying spatio-temporal patterns in classical and quantum systems out of equilibrium
• Verifying a quasi-classical spin model of perturbed quantum rewinding in a Fermi gas
• Lindblad quantum dynamics from correlation functions of classical spin chains
• Classical periodic trajectories and quantum scars in many-spin systems
• Topological floating phase of dipolar bosons in an optical ladder
• Bridging Quantum and Classical Descriptions of Spin Dynamics in a Dzyaloshinsky-Moriya Trimer
• Adiabaticity enhancement in the classical transverse field Ising chain, and its effective non-Hermitian description