Gräßer, TimoBleicker, PhilipHering, Dag-BjörnYarmohammadi, MohsenUhrig, Götz S.2021-12-142021-12-142021-12-10http://hdl.handle.net/2003/40603http://dx.doi.org/10.17877/DE290R-22473A 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=12 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.enDipolar interactionNitrogen vacancy centers in diamondDynamical mean field theoryHeisenberg modelAtomic, molecular & opticalStatistical physicsCondensed matter & materials physicsQuantum information530TextDipol-Dipol-WechselwirkungGitterbaufehlerStickstoffDiamantstrukturHeisenberg-ModellStatistische PhysikMonte-Carlo-SimulationSpinDynamische MolekularfeldtheorieKondensierte MaterieFestkörperphysik