Localization of Pairs in One-Dimensional Quasicrystals with Power-Law Hopping

TL;DR

This paper investigates how power-law hopping affects pair localization in one-dimensional quasicrystals, revealing symmetry breaking and different localization behaviors for attractive and repulsive interactions.

Contribution

It demonstrates the breaking of symmetry in pair localization due to power-law hopping and characterizes the contrasting behaviors of bound states under various conditions.

Findings

Power-law hopping breaks the symmetry in pair localization.

Repulsive bound states localize at or below the Aubry-Andre9 critical point.

Attractive bound states localize at larger quasiperiodic modulations with increasing hopping range.

Abstract

Pair localization in one-dimensional quasicrystals with nearest-neighbor hopping is independent of whether short-range interactions are repulsive or attractive. We numerically demonstrate that this symmetry is broken when the hopping follows a power law $1/r^{\alpha}$. In particular, for repulsively bound states, we find that the critical quasiperiodicity that signals the transition to localization is always bounded by the standard Aubry-Andr\'e critical point, whereas attractively bound dimers get localized at larger quasiperiodic modulations when the range of the hopping increases. Extensive numerical calculations establish the contrasting nature of the pair energy gap for repulsive and attractive interactions, as well as the behavior of the algebraic localization of the pairs as a function of quasiperiodicity, interaction strength, and power-law hops. The results here discussed are of direct relevance to the study of the quantum dynamics of systems with power-law couplings.