A new class of exact mobility edges in non-Hermitian quasiperiodic models

TL;DR

This paper introduces a novel method for exactly determining mobility edges in 1D non-Hermitian quasiperiodic models with $ ext{PT}$ symmetry, revealing a link between localization and symmetry breaking, and proposing an experimental detection scheme.

Contribution

The authors develop a new approach to find exact mobility edges in non-Hermitian quasiperiodic systems, advancing understanding of localization and phase transitions in such models.

Findings

Exact mobility edge determined for a specific non-Hermitian quasiperiodic model

Metal-insulator transition coincides with $ ext{PT}$-symmetry breaking transition

Proposed experimental protocol for observing localized states in photonic lattices

Abstract

Quantum localization in 1D non-Hermitian systems, especially the search for exact single-particle mobility edges, has attracted considerable interest recently. While much progress has been made, the available methods to determine the ME of such models are still limited. In this work, we propose a new method to determine the exact mobility edge in a large class of 1D non-Hermitian quasiperiodic models with parity-time ($\mathcal{PT}$) symmetry. We illustrate our method by studying a specific model. We first use our method to determine the energy-dependent mobility edge as well as the spectrum for localized eigenstates in this model. We then demonstrate that the metal-insulator transition must occur simultaneously with the spontaneous $\mathcal{PT}$-symmetry breaking transition in this model. Finally, we propose an experimental protocol based on a 1D photonic lattice to distinguish the extended and localized single-particle states in our model.