Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems

Abstract

We provide a detailed comparison between the dynamics of high-temperature spatiotemporal correlation functions in quantum and classical spin models. In the quantum case, our large-scale numerics are based on the concept of quantum typicality, which exploits the fact that random pure quantum states can faithfully approximate ensemble averages, allowing the simulation of spin-$1/2$ systems with up to $40$ lattice sites. Due to the exponentially growing Hilbert space, we find that for such system sizes even a single random state is sufficient to yield results with extremely low noise that is negligible for most practical purposes. In contrast, a classical analog of typicality is missing. In particular, we demonstrate that, in order to obtain data with a similar level of noise in the classical case, extensive averaging over classical trajectories is required, no matter how large the system size. Focusing on (quasi-)one-dimensional spin chains and ladders, we find a remarkably good agreement between quantum and classical dynamics. This applies not only to cases where both the quantum and classical model are nonintegrable, but also to cases where the quantum spin-$1/2$ model is integrable and the corresponding classical $s\to \infty$ model is not. Our analysis is based on the comparison of space-time profiles of the spin and energy correlation functions, where the agreement is found to hold not only in the bulk but also in the tails of the resulting density distribution. The mean-squared displacement of the density profiles reflects the nature of emerging hydrodynamics and is found to exhibit similar scaling for quantum and classical models.

14 pages, 9 figures

References in corpus (13)

• Thermalization and its mechanism for generic isolated quantum systems
• The Kernel Polynomial Method
• Open XXZ spin chain: Nonequilibrium steady state and strict bound on ballistic transport
• Spin transport in a one-dimensional anisotropic Heisenberg model
• Exact scaling functions for one-dimensional stationary KPZ growth
• Typicality for Generalized Microcanonical Ensembles
• Kardar-Parisi-Zhang physics in the quantum Heisenberg magnet
• Quantum dynamics of thermalizing systems
• Random phase vector for calculating the trace of a large matrix
• Lectures on the Bethe Ansatz
• Typicality of Prethermalization
• Decay of spin-spin correlations in disordered quantum and classical spin chains
• Effectiveness of classical spin simulations for describing NMR relaxation of quantum spins