Types of dynamical behavior in a quasiperiodic mosaic lattice
arXiv:2408.11765 · doi:10.1103/PhysRevB.111.014303
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.
11 pages, 7 figures
References in corpus (22)
- Anderson Transitions
- Nearest neighbor tight binding models with an exact mobility edge in one dimension
- Universal properties of hard-core bosons confined on one-dimensional lattices
- Ground-state properties of hard-core bosons confined on one-dimensional optical lattices
- Exact new mobility edges between critical and localized states
- Critical phase dualities in 1D exactly-solvable quasiperiodic models
- Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
- Dynamical observation of mobility edges in one-dimensional incommensurate optical lattices
- Dynamical Anderson transition in one-dimensional periodically kicked incommensurate lattices
- Self-consistent theory of mobility edges in quasiperiodic chains
- Generic mobility edges in several classes of duality-breaking one-dimensional quasiperiodic potentials
- Multiple localization transitions and novel quantum phases induced by staggered on-site potential
- Exact mobility edges for 1D quasiperiodic models
- Emergence of multifractality through cascade-like transitions in a mosaic interpolating Aubry-André-Fibonacci chain
- Engineering mobility in quasiperiodic lattices with exact mobility edges
- Periodically driven model with quasiperiodic potential and staggered hopping amplitudes: engineering of mobility gaps and multifractal states
- Probing multi-mobility edges in quasiperiodic mosaic lattices
- Strong-disorder renormalization-group study of the one-dimensional tight-binding model
- Coexistence of extended and localized states in finite-sized mosaic Wannier-Stark lattices
- Localization, multifractality, and many-body localization in periodically kicked quasiperiodic lattices
- Ground-state and dynamic properties of hard-core bosons in one-dimensional incommensurate optical lattices with harmonic trap
- Numerical Investigation of Localization in Two-Dimensional Quasiperiodic Mosaic Lattice