  We study the effects of interparticle interactions and power-law tunneling
couplings on quantum walks executed by both a single one and a pair of
hard-core bosons moving in clean and disordered one-dimensional lattices. For
this purpose, we perform exact diagonalization to explicitly evaluate the short
and long time probabilities of finding the walkers within a surveillance area.
Our main conclusions, summarized in phase diagrams in the disorder-power-law
and interaction-disorder spaces, allowed us to discern two different scenarios
for the single and two quantum walkers dynamics. While in the single particle
case the transition to localized and extended regimes is identified for well
defined values of the disorder amplitude and power law hopping, those frontiers
are replaced by diffuse contours in the interacting two particle case. In fact,
counterintuitive transport regimes as diffusion enhanced by disorder, and space
constrained dynamics assisted by both interactions and short tunneling range
are found. Our results are of direct relevance for quantum systems with
long-range interactions that are currently realized in the laboratory.
