Classical spin simulations with a quantum two-spin correction

Abstract

Classical simulations of high-temperature nuclear spin dynamics in solids are known to accurately predict relaxation for spin 1/2 lattices with a large number of interacting neighbors. Once the number of interacting neighbors becomes four or smaller, classical simulations lead to noticeable discrepancies. Here we attempt to improve the performance of the classical simulations by adding a term representing two-spin quantum correlations. The method is tested for a spin-1/2 chain. It exhibits good performance at shorter times, but, at longer times, it is hampered by a singular behavior of the resulting equations of motion.

Solid-State NMR Free Induction Decay, Simulated by the System of Classical Magnetic Moments and Quantum Correlations

“…At the same time, the TCF calculations for NMR turned out to be in demand in the study of the propagation of correlations in paramagnetic spin systems in the implementation of the numerical register. For example, in [13][14][15], the possibilities of matching and hybridization of quantum mechanical and classical calculations were considered. In particular, the method developed in these works made it possible to achieve good results for the FID of small quasi-onedimensional lattices.…”

“…We take the SPS system as a measuring basis in ( 11) and perform a POVM on the first spin, which reduces to multiplying on the SPS and computing the trace. As a result, we obtain the classical probability density function of the distribution over the values of the angles: (15) Now, to calculate the Shannon entropy, we have to calculate the integral over the Bloch sphere:…”

“…The mutual information calculated by formulas (10), (13), and (15) for this matrix will serve as a measure of the classical correlations. However, the obtained value depends on the chosen basis (11).…”