Non-Hermitian Maryland Model

TL;DR

This paper introduces an exactly solvable non-Hermitian extension of the Maryland model, revealing complex phase transitions and topological mobility edges in a quasi-crystal system, advancing understanding of non-Hermitian localization phenomena.

Contribution

It presents a novel exactly solvable non-Hermitian quasi-crystal model extending the classic Maryland model, uncovering new localization and topological phase transition features.

Findings

Reveals localization-delocalization phase transition in the non-Hermitian model

Identifies topological mobility edges in the complex energy plane

Shows richer phase transition scenarios compared to Hermitian counterparts

Abstract

Non-Hermitian systems with aperiodic order display phase transitions that are beyond the paradigm of Hermitian physics. Unfortunately, owing to the incommensurability of the potential most of known non-Hermitian models are not integrable. This motivates the search for exactly solvable models, where localization/delocalization phase transitions, mobility edges in complex plane and their topological nature can be unraveled. Here we present an exactly solvable model of quasi crystal, which is a non-pertrurbative non-Hermitian extension of a famous integrable model of quantum chaos proposed by Grempel {\it at al.} [Phys. Rev. Lett. {\bf 49}, 833 (1982)] and dubbed the Maryland model. Contrary to the Hermitian Maryland model, its non-Hermitian extension shows a richer scenario, with a localization-delocalization phase transition via topological mobility edges in complex energy plane.