Collection of algorithms concerning spin dynamic mean-field theory

The simulation of large interacting spin systems is a notoriously difficult task and requires the use of sophisticated approximation schemes. 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. This process is repeated until convergence is achieved. As the procedure requires only about 5 iteration steps, spinDMFT proves to be an efficient and powerful simulation tool for high-temperature spin systems. It can be extended to spin clusters (CspinDMFT), which improves the accuracy at the cost of higher computational effort. Another possible extension is non-local spinDMFT (nl-spinDMFT), which efficiently accesses non-local quantities such as spin pair correlations. This can be useful, for example, to compute free-induction decays.

This repository contains an implementation of the methods spinDMFT and its extensions CspinDMFT and nl-spinDMFT. The codes are written in C++.