Defects and degeneracies in supersymmetry protected phases

We analyse a class of 1D lattice models, known as M-k models, which are characterised by an order-k clustering of spin-less fermions and by N = 2 lattice supersymmetry. Our main result is the identification of a class of (bulk or edge) defects, that are in one-to-one correspondence with so-called spin fields in a corresponding Z(k) parafermion CFT. In the gapped regime, injecting such defects leads to ground-state degeneracies that are protected by the supersymmetry. The defects, which are closely analogous to quasi-holes over the fermonic Read-Rezayi quantum Hall states, display characteristic fusion rules, which are of Ising type for k = 2 and of Fibonacci type for k = 3.