  Phase frustration in periodic lattices is responsible for the formation of
dispersionless flat bands. The absence of any kinetic energy scale makes flat
band physics critically sensitive to perturbations and interactions. We report
here on the experimental investigation of the nonlinear dynamics of cavity
polaritons in the gapped flat band of a one-dimensional Lieb lattice. We
observe the formation of gap solitons with quantized size and very abrupt
edges, signature of the frozen propagation of switching fronts. This type of
gap solitons belongs to the class of truncated Bloch waves, and had only been
observed in closed systems up to now. Here the driven-dissipative character of
the system gives rise to a complex multistability of the nonlinear domains
generated in the flat band. These results open up interesting perspective
regarding more complex 2D lattices and the generation of correlated photon
phases.
