Localization and delocalization in one-dimensional systems with translation-invariant hopping
arXiv:2011.01008 · doi:10.1103/PhysRevB.103.L020201
Abstract
We present a theory of Anderson localization on a one-dimensional lattice with translation-invariant hopping. We find by analytical calculation, the localization length for arbitrary finite-range hopping in the single propagating channel regime. Then by examining the convergence of the localization length, in the limit of infinite hopping range, we revisit the problem of localization criteria in this model and investigate the conditions under which it can be violated. Our results reveal possibilities of having delocalized states by tuning the long-range hopping.
arXiv comment5 pages, 3 figures
References in corpus (11)
- Anderson Transitions
- Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
- Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
- Correlation-induced localization
- Duality in power-law localization in disordered one-dimensional systems
- Shielding and localization in presence of long range hopping
- Localization properties of a one-dimensional tight-binding model with non-random long-range inter-site interactions
- Spectral properties of distance matrices
- Anderson localization on a simplex
- Anderson localization of one-dimensional hybrid particles
- Irrational anomalies in one-dimensional Anderson localization