Competing Localizations on Disordered Non-Hermitian Random Graph Lattice

TL;DR

This paper investigates how localization phenomena in disordered non-Hermitian lattice systems are influenced by topology, randomness, and non-Hermiticity, revealing coexistence of different localization mechanisms and implications for complex networks.

Contribution

It introduces a generalized random graph lattice model to study the interplay of topology, disorder, and non-Hermiticity in localization transitions, including the non-Hermitian skin effect.

Findings

Skin effect and Anderson localization can coexist even under strong disorder.

Varying parameters reveals competition between different localization mechanisms.

Results have implications for machine learning and complex network information propagation.

Abstract

Phase transitions in one-dimensional lattice systems are well established and have been extensively studied within both Hermitian and non-Hermitian frameworks. In this work, we extend this understanding to a more general setting by investigating localization and delocalization transitions and the behavior of the non-Hermitian skin effect (NHSE) using a tight-binding model on a generalized random graph lattice. Our model incorporates three key parameters, asymmetric hopping $\Delta$, on-site disorder $W$, and a random long-range coupling $p$ that together define the underlying random graph structure. By varying $p$, $\Delta$, and the disorder strength, we explore the interplay between topology, randomness, and non-Hermiticity in determining localization properties. Our results show a strong competition between skin effect driven and Anderson driven localizations across parameter regimes. Notably, even in the presence of strong disorder, skin effect driven localization coexists with Anderson-driven localization. We further discuss the relevance of these results to machine-learning architectures and information propagation in complex networks and other real-world problems.