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We investigate the high-temperature dynamical conductivity $\sigma(\omega)$in two one-dimensional integrable quantum lattice models: the anisotropic XXZspin chain and the Hubbard chain. The emphasis is on the metallic regime ofboth models, where besides the ballistic component, the regular part ofconductivity might reveal a diffusive-like transport. To resolve thelow-frequency dynamics, we upgrade the microcanonical Lanczos method enablingstudies of finite-size systems with up to $L\leq 32$ sites for XXZ spin modelwith the frequency resolution $\delta \omega \sim 10^{-3} J$. Results for theXXZ chain reveal a fine structure of $\sigma(\omega)$ spectra, which originatesfrom the discontinuous variation of the stiffness, previously found atcommensurate values of the anisotropy parameter $\Delta$. Still, we do not finda clear evidence for a diffusive component, at least not for commensuratevalues of $\Delta$, particularly for $\Delta =0.5$, as well as for $\Delta \to0$. Similar is the conclusion for the Hubbard model away from half-filling,where the spectra reveal more universal behavior.

Coexistence of diffusive and ballistic transport in integrable quantum lattice models