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arXiv · 2107.07821

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

Timo Gräßer·Philip Bleicker·Dag-Björn Hering·Mohsen Yarmohammadi·Götz S. Uhrig
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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 $S = \tfrac12$ 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.

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Timo Gräßer, Philip Bleicker, Dag-Björn Hering, Mohsen Yarmohammadi, Götz S. Uhrig. 2021-07-16. Dynamic mean-field theory for dense spin systems at infinite temperature. https://doi.org/10.1103/physrevresearch.3.043168

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