Exploring localization properties in a folded N x N network on a cylinder’s shape with diagonal disorder and long-range hopping

In this work, we employ the inverse power method (IPM), a well-established technique in linear algebra, to investigate the quantum dynamics of a one-electron Hamiltonian in a unique geometric setup. Specifically, we consider a two-dimensional $N\times N$ lattice folded into a cylindrical topology, incorporating diagonal disorder and long-range hopping with a power-law decay. Unlike conventional studies that consider two-dimensional planar lattices, our model explicitly incorporates the curvature of the cylindrical geometry, enabling us to examine its potential influence on electronic properties. By analyzing the interplay between disorder, long-range hopping, and the system’s intrinsic curvature, our results suggest that geometry may play a role in the localization and transport behavior of electrons. These findings provide insights into how geometric factors could affect quantum systems, with potential implications for materials science and nanostructures exhibiting curved geometries.