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Theoretically challenging, the understanding of the dynamical response inquantum antiferromagnets is of great interest, in particular for both inelasticneutron scattering (INS) and nuclear magnetic resonance (NMR) experiments. Insuch a context, we theoretically address this question forquasi-one-dimensional quantum magnets, e.g. weakly coupled spin chains forwhich many compounds are available in Nature. In this class of systems, thedimensional crossover between a three-dimensional ordered regime at lowtemperature towards one-dimensional physics at higher temperature is anon-trivial issue, notably difficult concerning dynamical properties. Here wepresent a comprehensive theoretical study based on both analytical calculations(bosonization + random phase and self-consistent harmonic approximations) andnumerical simulations (quantum Monte Carlo + stochastic analytic continuation)which allows us to describe the full temperature crossover for the NMRrelaxation rate $1/T_1$, from one-dimensional Tomonaga-Luttinger liquid physicsto the three-dimensional ordered regime, as a function of inter-chaincouplings. The dynamical structure factor, directly probing the INS intensity,is also computed in the different regimes.

Dynamical response and dimensional crossover for spatially anisotropic antiferromagnets