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.