Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model
Abstract
In this study, we perform a detailed investigation into the interplay between disorder-induced electron localization and long-range hopping amplitudes within the Selective Long-Range Tight-Binding Model (SLRTB). Through numerical simulations, we analyze the electronic properties of the system, with a focus on the participation ratio (PR), entanglement entropy (EE), energy spectrum, and the ratio of level spacings (). Our results reveal a marked distinction between negative and positive long-range hopping amplitudes, manifesting in different electronic behaviors and transitions. Notably, we carry out a finite-size scaling analysis, identifying the critical point and exponents that characterize the system's behavior near the transition. The investigation highlights the role of gapless regions in shaping the system's PR, , and EE, and the influence of disorder on these properties. The SLRTB model proves to be an effective framework for understanding the effects of disorder and long-range hopping on electron dynamics, offering valuable insights into localization and delocalization phenomena.
Cite
@article{arxiv.2503.08132,
title = {Probing Electron Localization and Delocalization in the Selective Long-Range Tight-Binding Model},
author = {Mohammad Pouranvari},
journal= {arXiv preprint arXiv:2503.08132},
year = {2025}
}