Probing localization in one-dimensional chains with quasiperiodic potentials using non-Hermitian vector potentials

Abstract

We study the Hatano-Nelson model, a non-Hermitian single-particle system with asymmetrical nearest-neighbor hopping that is characterized by an imaginary vector potential, as a means of probing localization in the corresponding Hermitian system. Making use of a numerical algorithm based on critical values of this vector potential, we extract the inverse localization lengths of a one-dimensional system with a quasiperiodic potential, i.e., the generalized Aubry-André-Harper model (which exhibits both delocalized and localized eigenstates in its spectra) and benchmark the results against the inverse participation ratio and the exact localization lengths obtained via the Thouless formula. We find qualitative and numerical agreement supporting the case for using the non-Hermitian vector potentials as an alternative method of computing the inverse localization length.