Spin-models, where the
N spins interact pairwise with a
SU(nf) symmetry preserving hamiltonian, famously simplify in the large
nf,
N limits, as derived by Sachdev and Ye when exploring mean-field behavior of spin-glasses. We present numerical evidence that for a large class of models, the large
nf limit is not necessary: the same dynamical equations can describe the relaxation processes at high temperatures for a set of classical models inspired from mean-field treatments of interacting dense neutrino gases, up to times set by the radius of convergence of the perturbation series for the correlation function. After a simple rescaling of time, the dynamics display a surprising universality, being identical for any value of
nf as long as the rank of the coupling matrix is small. As a corollary of our results, we find that the direct interaction approximation originating from the study of stochastic flows in fluid turbulence should be thought of as only a short-time approximation for generic random coupling systems.
Ultra-fast spectroscopy can reveal the interplay of charges with low energy degrees of freedom, which underlies the rich physics of correlated materials. As a potential glue for superconductivity, spin fluctuations in Mott insulators are of particular interest. A theoretical description of the coupled spin and charge degrees of freedom is challenging, because magnetic order is often only short-lived and short-ranged. In this work we theoretically investigate how the spin-charge interactions influence the relaxation of a two-dimensional Mott-Hubbard insulator after photo-excitation. We use a nonequilibrium variant of the dynamical cluster approximation, which, in contrast to single-site dynamical mean-field theory, captures the effect of short-range correlations. The relaxation time is found to scale with the strength of the nearest-neighbor spin correlations, and can be 10-20 fs in the cuprates. Increasing the temperature or excitation density decreases the spin correlations and thus implies longer relaxation times. This may help to distinguish the effect of spin-fluctuations on the charge relaxation from the influence of other bosonic modes in the solid.