Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals

Abstract

The Lyapunov exponent, serving as an indicator of the localized state, is commonly utilized to identify localization transitions in disordered systems. In non-Hermitian quasicrystals, the non-Hermitian effect induced by non-reciprocal hopping can lead to the manifestation of two distinct Lyapunov exponents on opposite sides of the localization center. Building on this observation, we here introduce a comprehensive approach for examining the localization characteristics and mobility edges of non-reciprocal quasicrystals, referred to as asymmetric transfer matrix analysis. We demonstrate the application of this method to three specific scenarios: the non-reciprocal Aubry-André model, the non-reciprocal off-diagonal Aubry-André model, and the non-reciprocal mosaic quasicrystals. This work may contribute valuable insights to the investigation of non-Hermitian quasicrystal and disordered systems.

12 pages, 4 figures

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• Measurement-Induced Entanglement Phase Transition in Free Fermion Systems
• Emergent multi-loop nested point gap in a non-Hermitian quasiperiodic lattice
• Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Fate of pseudo mobility-edge and multiple states in non-Hermitian Wannier-Stark lattice
• Controlled probing of localization effects in the non-Hermitian Aubry-André model via topolectrical circuits
• Exact mobility line and mobility ring in the complex energy plane of a flat band lattice with a non-Hermitian quasiperiodic potential
• Anderson-skin dualism: A boundary-dependent effect in non-Hermitian disordered coupled systems
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Generalized Aubry-André-Harper model with power-law quasiperiodic potentials
• Controlled Zeno-Induced Localization of Free Fermions in a Quasiperiodic Chain