Types of dynamical behavior in a quasiperiodic mosaic lattice

Abstract

Quasiperiodic mosaic systems with the quasiperiodic potential being added periodically with a fixed lattice interval have attracted significant attention due to their peculiar spectral properties with exactly known mobility edges, which separate localized from delocalized states. These mobility edges do not vanish even in the region of large quasiperiodic potential strength, although the width of the energy window of extended states decreases with the increase in potential strength and thus becomes very narrow in the limit of strong quasiperiodic disorder. In this paper, we study the dynamics of a quasiperiodic mosaic lattice and unravel its peculiar dynamical properties. By scrutinizing the expansion dynamics of wave packet and the evolution of density distribution, we unveil that the long-time density distribution displays obviously different behaviors at odd and even sites in the region of large quasiperiodic potential strength. Particularly, the timescale of dynamics exhibits an inverse relationship with the quasiperiodic potential strength. To understand these behaviors, we derive an effective Hamiltonian in the large quasiperiodic potential strength region, which is composed of decoupled Hamiltonians defined on the odd and even sites, respectively. While all eigenstates of the effective Hamiltonian defined on even sites are localized, the eigenstates of effective Hamiltonian defined on odd sites include both localized and extended eigenstates. Our results suggest that the effective Hamiltonian can describe the dynamical behaviors well in the large quasiperiodic potential strength region and provides an intuitive framework for understanding the peculiar dynamical behaviors in the quasiperiodic mosaic lattice.