2025/11/13 by Rahul, S, A. Harshitha, Harshitha, A
Physics and Astronomy · #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Mechanics and Non-Hermitian Physics #Quantum Physics (quant-ph) #Quantum many-body systems #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2511.10156
openalex publication_date 2025/11/13 · openalex created_date 2025/11/15 · openalex updated_date 2026/07/28
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 Δ, on-site disorder W, and a random long-range coupling p that together define the underlying random graph structure. By varying p, Δ, 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.