Dynamic mean-field theory for dense spin systems at infinite temperature

Abstract

A dynamic mean-field theory for spin ensembles (spinDMFT) at infinite temperatures on arbitrary lattices is established. The approach is introduced for an isotropic Heisenberg model with $S=\frac{1}{2}$ and external field. For large coordination numbers, it is shown that the effect of the environment of each spin is captured by a classical time-dependent random mean-field which is normally distributed. Expectation values are calculated by averaging over these mean-fields, i.e., by a path integral over the normal distributions. A self-consistency condition is derived by linking the moments defining the normal distributions to spin autocorrelations. In this framework, we explicitly show how the rotating wave approximation becomes a valid description for increasing magnetic field. We also demonstrate that the approach can easily be extended. Exemplarily, we employ it to reach a quantitative understanding of a dense ensemble of spins with dipolar interaction which are distributed randomly on a plane including static Gaussian noise as well.

33 pages, 37 figures

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Cited by in corpus (7)

• Controlling local thermalization dynamics in a Floquet-engineered dipolar ensemble
• Performance of quantum registers in diamond in the presence of spin impurities
• Understanding the dynamics of randomly positioned dipolar spin ensembles
• Landau-Lifshitz damping from Lindbladian dissipation in quantum magnets
• Microscopic understanding of NMR signals by dynamic mean-field theory for spins
• First-principles simulation of spin diffusion in static solids using dynamic mean-field theory
• Influence of quadrupolar interaction on NMR spectroscopy