  We explore the relaxation dynamics of elementary spin clusters of a
kinetically constrained spin system. Inspired by experiments with Rydberg
lattice gases, we focus on the situation in which an excited spin leads to a
"facilitated" excitation of a neighboring spin. We show that even weak
interactions that extend beyond nearest neighbors can have a dramatic impact on
the relaxation behavior: they generate a linear potential, which under certain
conditions leads to the onset of Bloch oscillations of spin clusters. These
hinder the expansion of a cluster and more generally the relaxation of
many-body states towards equilibrium. This shows that non-ergodic behavior in
kinetically constrained systems may occur as a consequence of the interplay
between reduced connectivity of many-body states and weak interparticle
interactions. We furthermore show that the emergent Bloch oscillations
identified here can be detected in experiment through measurements of the
Rydberg atom density, and discuss how spin-orbit coupling between internal and
external degrees of freedom of spin clusters can be used to control their
relaxation behavior.
