One-dimensional quasicrystals with power-law hopping

TL;DR

This paper investigates one-dimensional quasi-periodic systems with power-law hopping, revealing unique localization and ergodicity transitions that differ from traditional models, with implications for experimental detection.

Contribution

It introduces a comprehensive analysis of power-law hopping effects in 1D quasi-periodic systems, highlighting new phases and transitions not seen in standard models.

Findings

Long-range hops with $a \,\leq\, 1$ do not localize states.

Systems exhibit ergodic, multifractal, and localized phases depending on parameters.

Expansion dynamics can experimentally reveal mobility and ergodic-to-multifractal edges.

Abstract

One-dimensional quasi-periodic systems with power-law hopping, $1/r^a$, differ from both the standard Aubry-Azbel-Harper (AAH) model and from power-law systems with uncorrelated disorder. Whereas in the AAH model all single-particle states undergo a transition from ergodic to localized at a critical quasi-disorder strength, short-range power-law hops with $a>1$ can result in mobility edges. Interestingly, there is no localization for long-range hops with $a\leq 1$, in contrast to the case of uncorrelated disorder. Systems with long-range hops are rather characterized by ergodic-to-multifractal edges and a phase transition from ergodic to multifractal (extended but non ergodic) states. We show that both mobility and ergodic-to-multifractal edges may be clearly revealed in experiments on expansion dynamics.