Anomalous and regular transport in spin-1/2 chains: ac conductivity

We study magnetization transport in anisotropic spin-1/2 chains governed by the integrable XXZ model with and without integrability-breaking perturbations at high temperatures (T -> infinity) using a hybrid approach that combines exact sum rules with judiciously chosen Ansatze. In the integrable XXZ model we find (i) superdiffusion at the isotropic (Heisenberg) point, with frequency dependent conductivity sigma' (omega -> 0) similar to vertical bar omega vertical bar(alpha), where alpha = -3/7 in close numerical agreement with recent t-DMRG computations; (ii) a continuously drifting exponent from alpha = -1(+) in the XY (gapless) limit of the model to alpha > 0 within the Ising (gapped) regime; and (iii) a diffusion constant saturating in the XY coupling deep in the Ising limit. We consider two kinds of next-nearest-neighbor integrability breaking perturbations-a simple spin-flip term (J(2)) and a three-spin assisted variant (t(2)), natural in the fermion particle representation of the spin chain. In the first case we discover a remarkable sensitivity of sigma' (omega) to the sign of J(2), with enhanced low frequency spectral weight and a pronounced upward shift in the magnitude of a for J(2) > 0. Perhaps even more surprising, we find subdiffusion (alpha > 0) over a range of J(2) < 0. By contrast, the effects of the fermionic three-spin perturbation are sign symmetric; this perturbation produces a clearly observable hydrodynamic relaxation. At large strength of the integrability breaking term J(2) -> +/-infinity the problem is effectively noninteracting (fermions hopping on odd and even sublattices) and we find alpha -> -1 behavior reminiscent of the XY limit of the integrable XXZ chain. Exact diagonalization studies largely corroborate these findings over accessible frequencies.