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Using the adaptive time-dependent density matrix renormalization groupmethod, we numerically study the spin dynamics and transport in one-dimensionalspin-1/2 systems at zero temperature. Instead of computing transportcoefficients from linear response theory, we study the real-time evolution ofthe magnetization starting from spatially inhomogeneous initial states. Inparticular, we are able to analyze systems far away from equilibrium with thisset-up. By computing the time-dependence of the variance of the magnetization,we can distinguish diffusive from ballistic regimes, depending on modelparameters. For the example of the anisotropic spin-1/2 chain and at halffilling, we find the expected ballistic behavior in the easy-plane phase, whilein the massive regime the dynamics of the magnetization is diffusive. Ourapproach allows us to tune the deviation of the initial state from the groundstate and the qualitative behavior of the dynamics turns out to be valid evenfor highly perturbed initial states in the case of easy-plane exchangeanisotropies. We further cover two examples of nonintegrable models, thefrustrated chain and the two-leg spin ladder, and we encounter diffusivetransport in all massive phases. In the former system, our results indicateballistic behavior in the critical phase. We discuss our findings in view ofexperiments on quasi-one dimensional quantum magnets and we propose that thestudy of the time-dependence of the spatial variance of particle densitiescould be instrumental in the characterization of the expansion of ultracoldatoms in optical lattices as well.

physical review. b, condensed matter and materials physics

A real-time study of diffusive and ballistic transport in spin-1/2  chains using the adaptive time-dependent density matrix renormalization group  method