Simulating the interplay of dipolar and quadrupolar interactions in NMR by spin dynamic mean-field theory

The simulation of nuclear magnetic resonance (NMR) experiments is a notoriously difficult task, if many spins participate in the dynamics. The recently established dynamic mean-field theory for high-temperature spin systems (spinDMFT) represents an efficient yet accurate method to deal with this scenario. SpinDMFT reduces a complex lattice system to a time-dependent single-site problem, which can be solved numerically with small computational effort. Since the approach retains local quantum degrees of freedom, a quadrupolar term can be exactly incorporated. This allows us to study the interplay of dipolar and quadrupolar interactions for any parameter range, i.e., without the need for a perturbative treatment. We obtain a remarkable agreement with experimental data for an aluminium nitride monocrystal, which strongly suggests the use of spinDMFT as a prediction tool. Furthermore, we draw a comparison between a quantum-mechanical and a classical version of spinDMFT showing that local quantum effects are of great importance for the studied type of system.

💡 Research Summary

This paper introduces and applies spin dynamic mean‑field theory (spinDMFT) to the simulation of nuclear magnetic resonance (NMR) experiments in dense, high‑temperature spin systems where both dipolar and quadrupolar interactions are relevant. Traditional exact diagonalisation quickly becomes infeasible because the Hilbert space grows exponentially with the number of spins, while classical simulations, although scalable, cannot capture the intrinsically quantum local effects introduced by the electric‑field‑gradient (EFG) coupling that generates the quadrupolar term. SpinDMFT overcomes these limitations by mapping the many‑body lattice problem onto a single‑site, time‑dependent Hamiltonian that retains the full quantum dynamics of a local spin while treating the surrounding environment as a Gaussian stochastic mean field.

The authors first define a microscopic model consisting of a secular dipolar Hamiltonian (H_{DD}= \frac12\sum_{i\neq j} d_{ij}