Tunable anomalous diffusion in anisotropic quantum spin chains from correlated initial states

Despite only hosting ballistically propagating quasiparticles, integrable systems can display diffusive transport at high temperatures. This diffusive behavior originates from the fact that fluctuations at high temperatures satisfy the central limit theorem. In this work, we examine the transport properties of anisotropic integrable spin chains in initial states whose fluctuations do not satisfy the central limit theorem. These so-called correlated initial states have fluctuations characterized by an exponent, w, known as the wandering exponent. We show that one can tune transport from subdiffusion to superdiffusion by changing the wandering exponent and provide a procedure to generate correlated initial states that will give a wandering exponent that either leads to subdiffusive, diffusive, or superdiffusive transport.