On transport properties of isotropic quasiperiodic XY spin chains

We consider isotropic $XY$ spin chains whose magnetic potentials are quasiperiodic and the effective one-particle Hamiltonians have absolutely continuous spectra. For a wide class of such $XY$ spin chains, we obtain lower bounds on their Lieb--Robinson velocities in terms of group velocities of their effective Hamiltonians: $\mathfrak v\ge\mathrm{ess\,sup}_{[0,1]} \frac{2}{\pi}\frac{dE}{dN},$ where $E$ is considered as a function of the integrated density of states.