Localization and mobility edges in the off-diagonal quasiperiodic model with slowly varying potentials

Abstract

We study a one-dimensional system that includes both a commensurate off-diagonal modulation of the hopping amplitude and an incommensurate, slowly varying diagonal on-site modulation. By using asymptotic heuristic arguments, we identify four closed form expressions for the mobility edges. We further study numerically the inverse participation ratio, the density of states and the Lyapunov exponent. The numerical results are in exact agreement with our theoretical predictions. Besides a metal-insulator transition driven by the strength of the slowly varying potential, another four insulator-metal transitions are found in this model as the energy is increased in magnitude from the band center ($E=0$) to the mobility edges ($\pm E_{c2},\pm E_{c1}$).

arXiv comment6 pages, 5 figures

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Cited by in corpus (13)

• Hidden dualities in 1D quasiperiodic lattice models
• Renormalization-Group Theory of 1D quasiperiodic lattice models with commensurate approximants
• Lyapunov exponent, mobility edges, and critical region in the generalized Aubry-Andre model with an unbounded quasiperiodic potential
• Novel mobility edges in the off-diagonal disordered tight-binding models
• Topological phase transition in the quasiperiodic disordered Su-Schriffer-Heeger chain
• Single-Particle Mobility Edge without Disorder
• Topological phases and Anderson localization in off-diagonal mosaic lattices
• Fate of topological states and mobility edges in one-dimensional slowly varying incommensurate potentials
• Majorana zero modes, unconventional real-complex transition and mobility edges in a one-dimensional non-Hermitian quasi-periodic lattice
• Proposed realization of critical regions in a one-dimensional flat band lattice with a quasi-periodic potential
• Invariable mobility edge in a quasiperiodic lattice
• Energy Spectrum Theory of Incommensurate Systems
• Exact mobility edges in a slowly varying quasiperiodic ladder model