On transport properties of isotropic quasiperiodic $XY$ spin chains

TL;DR

This paper investigates transport properties of isotropic quasiperiodic XY spin chains with absolutely continuous spectra, establishing lower bounds on Lieb-Robinson velocities based on the group velocities of their effective Hamiltonians.

Contribution

It provides a novel lower bound on Lieb-Robinson velocities for quasiperiodic XY spin chains using spectral analysis of their effective Hamiltonians.

Findings

Lower bounds on Lieb-Robinson velocities derived

Connection established between velocities and spectral properties

Applicable to a wide class of quasiperiodic XY chains

Abstract

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.