  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.
