High temperature dynamics in quantum compass models

We analyze the high temperature spin dynamics of compass models using a moment expansion. We point out that the evaluation of moments maps to the enumeration of paths in a branching process on the lattice. This mapping to a statistical mechanics combinatorics problem provides an elegant visualization of the analysis. We present results for the time dependent spin correlation function (which is of relevance to NMR experiments) for two compass models: the Kitaev honeycomb model and two-dimensional compass model.