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

TL;DR

This paper introduces a universal mapping technique that connects one-dimensional non-Hermitian mosaic models to their non-mosaic versions, enabling the derivation of mobility edges and Lyapunov exponents based on known properties of the latter.

Contribution

The authors develop a general mapping method that relates non-Hermitian mosaic models to non-mosaic models, facilitating analysis of localization properties.

Findings

Successfully derived mobility edges for mosaic models

Calculated Lyapunov exponents in mosaic models

Validated the mapping with two non-Hermitian models

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-Andr\'e-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.