Effectiveness of classical spin simulations for describing NMR relaxation of quantum spins

Abstract

We investigate the limits of effectiveness of classical spin simulations for predicting free induction decays (FIDs) measured by solid-state nuclear magnetic resonance (NMR) on systems of quantum nuclear spins. The specific limits considered are associated with the range of interaction, the size of individual quantum spins and the long-time behavior of the FID signals. We compare FIDs measured or computed for lattices of quantum spins (mainly spins 1/2) with the FIDs computed for the corresponding lattices of classical spins. Several cases of excellent quantitative agreement between quantum and classical FIDs are reported along with the cases of gradually decreasing quality of the agreement. We formulate semi-empirical criteria defining the situations, when classical simulations are expected to accurately reproduce quantum FIDs. Our findings indicate that classical simulations may be a quantitatively accurate tool of first principles calculations for a broad class of macroscopic systems, where individual quantum microscopic degrees of freedom are far from the classical limit.

arXiv comment6 pages, 3 figures

References in corpus (14)

• Regression relation for pure quantum states and its implications for efficient computing
• Dynamic correlations of antiferromagnetic spin-1/2 XXZ chains at arbitrary temperature from complete diagonalization
• Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2
• Largest Lyapunov exponents for lattices of interacting classical spins
• Universal Long-time Behavior of Nuclear Spin Decays in a Solid
• Long-time Behavior of Nuclear Spin Decays in Various Lattices
• Signatures of Chaos in Time Series Generated by Many-Spin Systems at High Temperatures
• Eigenmodes in the long-time behavior of a coupled spin system measured with nuclear magnetic resonance
• Spin transport in the XXZ model at high temperatures: Classical dynamics versus quantum S=1/2 autocorrelations
• Dipolar-broadening of I=1/2-NMR spectra of solids
• Long-Time Relaxation on Spin Lattice as Manifestation of Chaotic Dynamics
• Lyapunov instabilities in lattices of interacting classical spins at infinite temperature
• Universal Long-Time Relaxation on the Lattices of Classical Spins: Markovian Behavior on non-Markovian Timescales
• NMR Spin-Spin Relaxation as Kinetics in Spin Phase Space

Cited by in corpus (12)

• Quantum versus Classical Dynamics in Spin Models: Chains, Ladders, and Square Lattices
• Quantum computation of molecular structure using data from challenging-to-classically-simulate nuclear magnetic resonance experiments
• Hybrid quantum-classical method for simulating high-temperature dynamics of nuclear spins in solids
• Free induction decays in nuclear spin-1/2 lattices with small number of interacting neighbors: the cases of silicon and fluorapatite
• Spatiotemporal dynamics of classical and quantum density profiles in low-dimensional spin systems
• Signatures of electronic correlations and spin-susceptibility anisotropy in nuclear magnetic resonance
• First-principles simulation of spin diffusion in static solids using dynamic mean-field theory
• Classical periodic trajectories and quantum scars in many-spin systems
• Microscopic understanding of NMR signals by dynamic mean-field theory for spins
• Cooling classical many-spin systems using feedback control
• Classical spin simulations with a quantum two-spin correction
• Lindblad quantum dynamics from correlation functions of classical spin chains