Supersymmetry in an interacting Majorana model on the kagome lattice

We construct a supersymmetric model of interacting Majorana fermions on the kagome lattice. In the infinite-coupling limit, the model exhibits an extensively degenerate ground state manifold separated in two topological sectors, in addition to two parity supersectors. An exact solution for thin-torus geometries allows us to analytically construct the entire zero-energy ground state manifold. Upon inclusion of hopping terms with energy scale g, the supersymmetry is spontaneously broken with the ground state energy density scaling as g(4). We also briefly discuss the noninteracting limit of the model, which exhibits a zero-energy flat band and Majorana Chern bands.