Collection of algorithms concerning spin dynamic mean-field theory

One possibility is the recently established dynamic mean-field theory for spins (spinDMFT). This method is developed for tackling dense high-temperature spin ensembles as they occur, for example, in nuclear magnetic resonance. "Dense" in this context means that each spin has a large number of interaction partners.

The key idea of spinDMFT is to replace the environment of a spin by a time-dependent Gaussian mean-field, thereby reducing the many-body problem to an effective single-site problem. The second moments of the mean-field are related to the spin's autocorrelation functions. This entails a self-consistency problem, which can be solved by numerical iteration: One starts with an initial guess for the mean-field moments, solves the single-site problem to compute the spin autocorrelations and uses the self-consistency condition to update the mean-field moments.