Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model

Abstract

Non-Hermitian effects could trigger spectrum, localization and topological phase transitions in quasiperiodic lattices. We propose a non-Hermitian extension of the Maryland model, which forms a paradigm in the study of localization and quantum chaos by introducing asymmetry to its hopping amplitudes. The resulting nonreciprocal Maryland model is found to possess a real-to-complex spectrum transition at a finite amount of hopping asymmetry, through which it changes from a localized phase to a mobility edge phase. Explicit expressions of the complex energy dispersions, phase boundaries and mobility edges are found. A topological winding number is further introduced to characterize the transition between different phases. Our work introduces a unique type of non-Hermitian quasicrystal, which admits exactly obtainable phase diagrams, mobility edges, and holding no extended phases at finite nonreciprocity in the thermodynamic limit.

8 pages, 3 figures, 1 table

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Cited by in corpus (15)

• Non-Hermitian skin effect and self-acceleration
• Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
• Driving-induced multiple $\mathcal{P}\mathcal{T}$-symmetry breaking transitions and reentrant localization transitions in non-Hermitian Floquet quasicrystals
• Entanglement phase transitions in non-Hermitian quasicrystals
• Non-Abelian generalization of non-Hermitian quasicrystal: PT-symmetry breaking, localization, entanglement and topological transitions
• Phase transitions and bunching of correlated particles in a non-Hermitian quasicrystal
• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Anomalous spectrum in a non-Hermitian quasiperiodic chain
• Phase transitions in non-Hermitian superlattices
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Coexistence of extended and localized states in one-dimensional non-Hermitian Anderson model