On Transport Properties of Isotropic Quasiperiodic XY Spin Chains

Abstract

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:where E is considered as a function of the integrated density of states.

Localization properties of the disordered XY spin chain

“…where M A and M B are restrictions of the effective Hamiltonian to A and B, respectively, and spectral projections analogous to (35) appear. Similar to above, now using eigencorrelator localization for M, M A and M B , this leads to (30).…”

Ballistic Transport and Absolute Continuity of One-Frequency Schrödinger Operators

“…In [12], the authors established lower bound for the Lieb-Robinson velocity for the anisotropic XY chain on Z with periodic parameters as an application of their proof of the ballistic motions. Also through this connection with Schrödinger operators, Kachkovskiy [22] has proven similar lower bound for a class of isotropic quasi-periodic XY spin, corresponding to analytic cocycles which are reducible for almost every energy, including the small analytic regime in [32], and the cases with purely a.c. spectrum and a single Diophantine frequency. It is explained in [22] that although the transport property in two models share some connections, the averaged lower bound of Guarneri-Combes-Last does not translate into useful informations for XY spin chains.…”

Spectral approximation for ergodic CMV operators with an application to quantum walks

“…The motivation for this paper came about as one of the authors was writing [14]; there had been a substantial amount of recent activity on the connection between various versions of ballistic motion and purely absolutely continuous (a.c.) spectrum for 1-dimensional operators (Schrödinger, Jacobi, and CMV) [2,11,14,20,34,35]. Since the methods of [14] produce ballistic motion for limit-periodic CMV matrices satisfying a Pastur-Tkachenko-like condition, we wanted to verify that such CMV matrices indeed had purely a.c. spectrum.…”