  Cold atoms coupled to photonic crystals constitute an exciting platform for
exploring quantum many-body physics. Here we investigate the strong coupling
between atomic internal ("spin") degrees of freedom and motion, which arises
from spin-dependent forces associated with the exchange of guided photons. We
show that this system can realize a remarkable and extreme limit of quantum
spin-orbital systems, where both the direct spin exchange between neighboring
sites and the kinetic energy of the orbital motion vanish. We find that this
previously unexplored system has a rich phase diagram of emergent orders,
including spatially dimerized spin-entangled pairs, a fluid of composite
particles comprised of joint spin-phonon excitations, phonon-induced N\'eel
ordering, and a fractional magnetization plateau associated with trimer
formation.
