First-principles simulation of spin diffusion in static solids using dynamic mean-field theory

The dynamics of disordered nuclear spin ensembles are the subject of nuclear magnetic resonance studies. Because of the through-space long-range dipolar interaction, generically, many spins are involved in the time evolution, so that exact brute force calculations are impossible. The recently established spin dynamic mean-field theory (spinDMFT) represents an efficient and unbiased alternative to overcome this challenge. The approach only requires the dipolar couplings as input, and the only prerequisite for its applicability is that each spin interacts with a large number of other spins. Here, we show that spinDMFT can be used to describe spectral spin diffusion in static samples and to simulate zero-quantum line shapes which eluded an efficient quantitative simulation so far to the best of our knowledge. We perform benchmarks for two test substances that establish an excellent match with published experimental data. As spinDMFT combines low computational effort with high accuracy, we suggest to use it for large-scale simulations of spin diffusion, which are important in various areas of magnetic resonance.