Supersymmetry in an interacting Majorana model on the kagome lattice*

We construct a supersymmetric model of interacting Majorana modes on the kagome lattice. The supersymmetry is manifest in the infinite-coupling limit, which exhibits an exponential ground state manifold separated in two parity "supersectors". An exact solution for thin torus geometries allows us to analytically construct the entire ground state manifold. Upon inclusion of weak two-fermion terms, the supersymmetry is broken for finite systems but recovered in the thermodynamic limit. We also briefly discuss the non-interacting limit of the model, which exhibits a zero-energy flat band and Majorana Chern bands.