Topological phases in gapped edges of fractionalized systems

Understand

Recently, it has been proposed that exotic one-dimensional phases can be realized by gapping out the edge states of a fractional topological insulator.

• The low-energy edge degrees of freedom are described by a chain of coupled parafermions.
• We introduce a classification scheme for the phases that can occur in parafermionic chains.
• We find that the parafermions support both topological symmetry fractionalized phases as well as phases in which the parafermions condense.