Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice

TL;DR

This paper analytically determines the exact non-Hermitian mobility edges in a one-dimensional quasiperiodic lattice with exponential decay hopping and complex potentials, revealing how non-Hermitian effects influence localization transitions.

Contribution

It provides an analytical derivation of the mobility edges in a non-Hermitian quasiperiodic lattice model using Avila's global theory, extending the understanding of localization in such systems.

Findings

Exact mobility edge expression derived for the non-Hermitian model

Dual transformation maps spectra and wavefunctions between models

Non-Hermitian term breaks self-duality symmetry

Abstract

We analytically determine the non-Hermitian mobility edges of a one-dimensional quasiperiodic lattice model with exponential decaying hopping and complex potentials as well as its dual model, which is just a non-Hermitian generalization of the Ganeshan-Pixley-Das Sarma model with nonreciprocal nearest-neighboring hopping. The presence of non-Hermitian term destroys the self-duality symmetry and thus prevents us exploring the localization-delocalization point through looking for self-dual points. Nevertheless, by applying Avila's global theory, the Lyapunov exponent of the Ganeshan-Pixley-Das Sarma model can be exactly derived, which enables us to get an analytical expression of mobility edge of the non-Hermitian dual model. Consequently, the mobility edge of the original model is obtained by using the dual transformation, which creates exact mappings between the spectra and wavefunctions of these two models.