Novel mobility edges in the off-diagonal disordered tight-binding models

Abstract

We study the one-dimensional tight-binding models which include a slowly varying, incommensurate off-diagonal modulation on the hopping amplitude. Interestingly, we find that the mobility edges can appear only when this off-diagonal (hopping) disorder is included in the model, which is different from the known results induced by the diagonal disorder. We further study the situation where the off-diagonal and diagonal disorder terms (the incommensurate potential) are both included and find that the locations of mobility edges change significantly and the varying trend of the mobility edge becomes nonsmooth. We first identify the exact expressions of mobility edges of both models by using asymptotic heuristic argument, and then verify the conclusions by utilizing several numerical diagnostic techniques, including the inverse participation ratio, the density of states and the Lyapunov exponent. This result will perspectives for future investigations on the mobility edge in low dimensional correlated disordered system.

arXiv comment6 pages,6 figures

References in corpus (25)

• Anderson localization of a non-interacting Bose-Einstein condensate
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Three-dimensional localization of ultracold atoms in an optical disordered potential
• Three-Dimensional Anderson Localization of Ultracold Matter
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Exploring the Single-Particle Mobility Edge in a One-Dimensional Quasiperiodic Optical Lattice
• Topological Zero-Energy Modes in Gapless Commensurate Aubry-André-Harper Models
• Delocalization of a disordered bosonic system by repulsive interactions
• Measurement of the mobility edge for 3D Anderson localization
• Mobility Edges in 1D Bichromatic Incommensurate Potentials
• Anderson localization in Bose-Einstein condensates
• Exponential localization in one-dimensional quasiperiodic optical lattices
• Topological superconductor to Anderson localization transition in one-dimensional incommensurate lattices
• Observation of a disordered bosonic insulator from weak to strong interactions
• Phase diagram of a non-Abelian Aubry-André-Harper model with $p$-wave superfluidity
• Quantum nonergodicity and fermion localization in a system with a single-particle mobility edge
• Mobility edge for cold atoms in laser speckle potentials
• Self-dual quasiperiodic systems with power-law hopping
• Anderson localization transitions with and without random potentials
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Quantum transport of atomic matterwaves in anisotropic 2D and 3D disorder
• Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials
• Fate of topological states and mobility edges in one-dimensional slowly varying incommensurate potentials
• Sensitivity of the entanglement spectrum to boundary conditions as a characterization of the phase transition from delocalization to localization

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