2017/11/30 by Ramsés J. Sánchez, Vipin Kerala Varma, Vadim Oganesyan · 1 citation
Physics and Astronomy · #cond-mat.mes-hall #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.98.054415
published as Phys. Rev. B 98, 054415 (2018) · 2-column format, 17 pages, 58 references, 8 figures
arxiv created 2018/03/05 · arxiv updated 2018/08/17
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→ ∞) using a hybrid approach that combines exact sum-rules with judiciously chosen Ansätze. In the integrable XXZ model we find (i) super-diffusion at the isotropic (Heisenberg) point, with frequency dependent conductivity σ'(ω→ 0) ∼ |ω|α, where α=-3/7 in close numerical agreement with recent t-DMRG computations; (ii) a continuously drifting exponent from α=-1+ in the XY limit of the model to α>0 within the Ising regime; and (iii) a diffusion constant saturating in the XY coupling deep in the Ising limit. We consider two kinds of integrability breaking perturbations --- a simple next-nearest-neighbor spin-flip term (J2) and a three-spin assisted variant (t2), natural in the fermion particle representation of the spin chain. In the first case we discover a remarkable sensitivity of σ'(ω) to the sign of J2, with enhanced low frequency spectral weight and a pronounced upward shift in the magnitude of α for J2>0. Perhaps even more surprising, we find sub-diffusion (α>0) over a range of J2<0. By contrast, the effects of the \enquotefermionic three-spin perturbation are sign symmetric; this perturbation produces a clearly observable hydrodynamic relaxation. At large strength of the integrability breaking term J2→ ± ∞ the problem is effectively non-interacting (fermions hopping on odd and even sublattices) and we find α→ -1 behavior reminiscent of the XY limit of the XXZ chain. Exact diagonalization studies largely corroborate these findings at mid-frequencies.