  One-dimensional quantum emitters with chiral couplings can exhibit
nonreciprocal decay channels, along with light-induced dipole-dipole
interactions mediated via an atom-waveguide interface. When the position
disorders are introduced to such atomic array, we are able to identify the
dynamical phase transition from excitation delocalization to localization, with
an interplay between the directionality of decay rates and the strength of
light-induced dipole-dipole interactions. Deep in the localization phase, its
characteristic length decreases and saturates toward a reciprocal coupling
regime, leading to a system dynamics whose ergodicity is strongly broken. We
also find an interaction-driven re-entrant behavior of the localization phase
and a reduction of level repulsion under strong disorder. The former coincides
with a drop in the exponent of power-law decaying von Neumann entropy, which
gives insights to a close relation between the preservation of entanglement and
nonequilibrium dynamics in open quantum systems, while the latter presents a
distinct narrow distribution of gap ratios in this particular disordered
system.
