Breakdown of the correspondence between the real-complex and delocalization-localization transitions in non-Hermitian quasicrystals

TL;DR

This paper investigates the relationship between spectral transitions and localization in non-Hermitian quasicrystals, revealing conditions where this correspondence breaks down or reemerges due to symmetry effects.

Contribution

It introduces a generalized Aubry-Andre9 model with off-diagonal modulation, showing breakdown and recovery of the real-complex and localization correspondence.

Findings

Breakdown of the correspondence with incommensurate off-diagonal modulation.

Emergence of an intermediate phase with a non-Hermitian mobility edge.

Reappearance of the correspondence when PT-symmetry is recovered.

Abstract

The correspondence between the real-complex transition in energy and delocalization-localization transition is well-established in a class of Aubry-Andr'e-Harper model with exponential non-Hermitian on-site potentials. In this paper, we study a generalized Aubry-Andr'e model with off-diagonal modulation and non-Hermitian on-site potential. We find that, when there exists an incommensurate off-diagonal modulation, the correspondence breaks down, although the extended phase is maintained in a wide parameter range of the strengths of the on-site potential and the off-diagonal hoppings. An additional intermediate phase with a non-Hermitian mobility edge emerges when the off-diagonal hoppings become commensurate. This phase is characterized by the real and complex sections of the energy spectrum corresponding to the extended and localized states. In this case, the aforementioned correspondence reappears due to the recovery of the PT-symmetry.