General mapping of one-dimensional non-Hermitian mosaic models to non-mosaic counterparts: Mobility edges and Lyapunov exponents

Abstract

We establish a general mapping from one-dimensional non-Hermitian mosaic models to their non-mosaic counterparts. This mapping can give rise to mobility edges and even Lyapunov exponents in the mosaic models if critical points of localization or Lyapunov exponents of localized states in the corresponding non-mosaic models have already been analytically solved. To demonstrate the validity of this mapping, we apply it to two non-Hermitian localization models: an Aubry-André-like model with nonreciprocal hopping and complex quasiperiodic potentials, and the Ganeshan-Pixley-Das Sarma model with nonreciprocal hopping. We successfully obtain the mobility edges and Lyapunov exponents in their mosaic models. This general mapping may catalyze further studies on mobility edges, Lyapunov exponents, and other significant quantities pertaining to localization in non-Hermitian mosaic models.

9 pages, 2 figures

References in corpus (21)

• Anderson Transitions
• Topological Origin of Non-Hermitian Skin Effects
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Topological phase transition in non-Hermitian quasicrystals
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Observation of arbitrary topological windings of a non-Hermitian band
• Observation of tunable mobility edges in generalized Aubry-André lattices
• Reentrant Localization Transition in a Quasiperiodic Chain
• Localization transition, spectrum structure and winding numbers for one-dimensional non-Hermitian quasicrystals
• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• Exact mobility edges, $\mathcal{P}\mathcal{T}$-symmetry breaking and skin effect in one-dimensional non-Hermitian quasicrystals
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Observation of interaction-induced mobility edge in a disordered atomic wire
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Boundary-dependent Self-dualities, Winding Numbers and Asymmetrical Localization in non-Hermitian Quasicrystals
• Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice
• Detecting non-Bloch topological invariants in quantum dynamics
• Duality between two generalized Aubry-Andre models with exact mobility edges
• Two dimensional vertex-decorated Lieb lattice with exact mobility edges and robust flat bands
• A general approach to the exact localized transition points of 1D mosaic disorder models

Cited by in corpus (5)

• Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
• Coexistence of ergodic and weakly ergodic states in finite-height Wannier-Stark ladders
• Exact non-Hermitian mobility edges and robust flat bands in two-dimensional Lieb lattices with imaginary quasiperiodic potentials
• Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems
• Generic non-Hermitian mobility edges in a class of duality-breaking quasicrystals