Although integrable spin chains host only ballistically propagating particles, they can still feature diffusive charge transfer. This diffusive charge transfer originates from quasiparticle charge fluctuations inherited from the initial state's magnetization Gaussian fluctuations. We show that ensembles of initial states with quasi-long-range correlations lead to superdiffusive charge transfer with a tunable dynamical exponent. We substantiate our prediction with numerical simulations and discuss how finite time and finite size effects might cause deviations.
Quantum-state transfer with fidelity higher than
0.99 can be achieved in the ballistic regime of an arbitrarily long one-dimensional chain with uniform nearest-neighbor interaction, except for the two pairs of mirror-symmetric extremal bonds, say
x (first and last) and
y (second and penultimate). These have to be roughly tuned to suitable values $x\ensuremath{\sim}2{N}^{\ensuremath{-}1/3}$ and $y\ensuremath{\sim}{2}^{3/4}{N}^{\ensuremath{-}1/6}$, where
N is the chain length. The general framework can describe the end-to-end response in different models, such as fermion or boson hopping models and
XX spin chains.
We study spin transport in a boundary driven XXZ spin chain. Driving at the chain boundaries is modeled by two additional spin chains prepared in oppositely polarized states. Emergent behavior, both in the transient dynamics and in the long-time quasi-steady state, is demonstrated. Time-dependent matrix-product-state simulations of the system-bath state show ballistic spin transport below the Heisenberg isotropic point. Indications of exponentially vanishing transport are found above the Heisenberg point for low energy initial states while the current decays asymptotically as a power law for high energy states. Precisely at the critical point, non-ballistic transport is observed. Finally, it is found that the sensitivity of the quasi-stationary state on the initial state of the chain is a good witness of the different transport phases.