  Artificial spin-orbit coupling in optical lattices can be engineered to tune
band structure into extreme regimes where the single-particle band flattens
leaving only inter-particle interactions to define many-body states of matter.
Lin et al. [Phys. Rev. Lett 112, 110404 (2014)] showed that under such
conditions interactions lead to a Wigner crystal of fermionic atoms under
approximate conditions: no bandwidth or band mixing. The excitations were shown
to possess emergent kinetics with fractionalized charge derived entirely from
interactions. In this work we use numerical exact diagonalization to study a
more realistic model with non-zero bandwidth and band mixing. We map out the
stability phase diagram of the Wigner crystal. We find that emergent properties
of the Wigner crystal excitations remain stable for realistic experimental
parameters. Our results validate the approximations made by Lin et al. and
define parameter regimes where strong interaction effects generate emergent
kinetics in optical lattices.
