Z$_N$ parafermion zero modes without Fractional Quantum Hall effect
  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. 
A.M. Tsvelik
cond-mat.str-el