Parafermion zero energy modes are a vital element of fault-tolerant topological quantum computation. Although it is believed that such modes form on the border between topological and normal phases, this has been demonstrated only for $Z_2$ (Majorana) and $Z_3$ parafermions. I consider an integrable model of one-dimensional fermions where such a demonstration is possible for $Z_N$ parafermions with any $N$. The procedure is easily generalizable for more complicated symmetry groups.

• Received 10 April 2014

DOI:https://doi.org/10.1103/PhysRevLett.113.066401