Coexistence of diffusive and ballistic transport in integrable quantum lattice models
P. Prelovšek, Marcin Mierzejewski, J. Herbrych
Abstract
We investigate the high-temperature dynamical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ in two one-dimensional integrable quantum lattice models: the anisotropic XXZ spin chain and the Hubbard chain. The emphasis is on the metallic regime of both models, where besides the ballistic component, the regular part of conductivity might reveal a diffusivelike transport. To resolve the low-frequency dynamics, we upgrade the microcanonical Lanczos method enabling studies of finite-size systems with up to $L\ensuremath{\le}32$ sites for the XXZ spin model with the frequency resolution $\ensuremath{\delta}\ensuremath{\omega}\ensuremath{\sim}{10}^{\ensuremath{-}3}J$. Results for the XXZ chain reveal a fine structure of $\ensuremath{\sigma}(\ensuremath{\omega})$ spectra, which originates from the discontinuous variation of the stiffness, previously found at commensurate values of the anisotropy parameter $\mathrm{\ensuremath{\Delta}}$. Still, we do not find clear evidence for a diffusive component, at least not for commensurate values of $\mathrm{\ensuremath{\Delta}}$, particularly for $\mathrm{\ensuremath{\Delta}}=0.5$, as well as for $\mathrm{\ensuremath{\Delta}}\ensuremath{\rightarrow}0$. Similar is the conclusion for the Hubbard model away from half-filling, where the spectra reveal more universal behavior.