Localization Properties of a Disordered Helical Chain

Abstract

We study the localization properties of the quasiperiodic one-dimensional helical chain with two tunneling paths: nearest-neighbor and a long-range hop that connects sites of consecutive helical turns. Using exact diagonalization, we quantify localization employing the inverse participation ratio (IPR) and the normalized participation ratio (NPR), and combine them into a single measure to create a phase map. The resulting diagrams reveal three regimes: a completely extended phase, a completely localized phase, and a mixed domain where localized and extended states coexist. In the diagrams, we investigate the behaviors of tightly and loosely wound helices and examine a special case where the number of sites per turn is a Fibonacci number. For moderate numbers of sites per helical turn, the mixed region is broad and also shifts with the long-range coupling. When the turn size is a Fibonacci number, the phase boundary becomes nearly horizontal and the mixed region fades out, effectively recovering the standard Aubry-André model behavior.

References in corpus (13)

• Anderson Transitions
• Anderson localization of a non-interacting Bose-Einstein condensate
• Observation of many-body localization of interacting fermions in a quasi-random optical lattice
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Direct observation of a localization transition in quasi-periodic photonic lattices
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• One-dimensional quasicrystals with power-law hopping
• Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
• Reentrant Localization Transition in a Quasiperiodic Chain
• Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials
• Bloch dynamics in lattices with long range hoppings
• Critical analysis of multiple reentrant localization in an antiferromagnetic helix with transverse electric field: Hopping dimerization-free scenario