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

• Main Authors: Sánchez, Ramsés J, Varma, Vipin Kerala, Oganesyan, Vadim
• Format: Journal Article
• Language: English
• Published: 05-03-2018
• Subjects: Physics - Mesoscale and Nanoscale Physics; Physics - Strongly Correlated Electrons
• DOI: 10.48550/arxiv.1711.11214

Phys. Rev. B 98, 054415 (2018) 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 ($T\to \infty$) using a hybrid approach that combines
exact sum-rules with judiciously chosen Ans\"atze. In the integrable XXZ model
we find (i) super-diffusion at the isotropic (Heisenberg) point, with frequency
dependent conductivity $ \sigma'(\omega\to 0) \sim |\omega|^{\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 limit of the
model to $\alpha>0$ 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 ($J_2$) 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 $\alpha$ for $J_2>0$. Perhaps even more surprising, we find
sub-diffusion ($\alpha>0$) over a range of $J_2<0$. By contrast, the effects of
the \enquote{fermionic} three-spin perturbation are sign symmetric; this
perturbation produces a clearly observable hydrodynamic relaxation. At large
strength of the integrability breaking term $J_2\to \pm \infty$ the problem is
effectively non-interacting (fermions hopping on odd and even sublattices) and
we find $\alpha\to -1$ behavior reminiscent of the XY limit of the XXZ chain.
Exact diagonalization studies largely corroborate these findings at
mid-frequencies.