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

TL;DR

This paper develops a dynamic mean-field theory for dense spin systems at infinite temperature, providing a new analytical framework to understand spin dynamics on arbitrary lattices, especially in high coordination regimes.

Contribution

It introduces a spinDMFT approach capturing environment effects via classical time-dependent random mean-fields, extending to systems with dipolar interactions and static noise.

Findings

Validates the rotating wave approximation at high magnetic fields

Provides a quantitative understanding of dense spin ensembles with dipolar interactions

Framework can be extended to various spin system configurations

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.