  We investigate phases of spinless fermions on the honeycomb lattice with
nearest neighbor interaction in the Hofstadter regime. The interaction induces
incompressible nematic and ferri-electric phases with broken translation
symmetry. Some of the transitions are accompanied by changes in the Hall
conductivity. We study pair correlations and show that the quantum metric,
averaged over the Brillouin zone, characterizes the shape of the pair
correlation function.
