Asymmetric transfer matrix analysis of Lyapunov exponents in one-dimensional non-reciprocal quasicrystals
arXiv:2407.01372 · doi:10.1103/PhysRevB.110.134203
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.
arXiv comment12 pages, 4 figures
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