  The electronic band structure of many compounds, e.g., carbon-based
structures, can exhibit essentially no dispersion. Models of electrons in
flat-band lattices define non-perturbative strongly correlated problems by
default. We construct a set of Jastrow-correlated ansatz wavefunctions to
capture the low energy physics of interacting particles in flat bands. We test
the ansatz in a simple Coulomb model of spinless electrons in a honeycomb
ribbon. We find that the wavefunction accurately captures the ground state in a
transition from a crystal to a uniform quantum liquid.
