Z${}_N$ parafermion zero modes without Fractional Quantum Hall effect

Abstract

I discuss a one-dimensional model of interacting fermions which collective excitations are Z${}_N$-parafermions. The phase diagram of this model contains ground states with Charge Density Wave and superconducting quasi long range order. Boundaries between these phases contain zero energy parafermion modes.

5 pages, Introduction and Conclusions sections expanded