  We introduce the concept of dark space phase transition, which may occur in
open many-body quantum systems where irreversible decay, interactions and
quantum interference compete. Our study is based on a quantum many-body model,
that is inspired by classical nonequilibrium processes which feature phase
transitions into an absorbing state, such as epidemic spreading. The
possibility for different dynamical paths to interfere quantum mechanically
results in collective dynamical behavior without classical counterpart. We
identify two competing dark states, a trivial one corresponding to a classical
absorbing state and an emergent one which is quantum coherent. We establish a
nonequilibrium phase transition within this dark space that features a
phenomenology which cannot be encountered in classical systems. Such emergent
two-dimensional dark space may find technological applications, e.g. for the
collective encoding of a quantum information.
