Interplay between intrinsic and emergent topological protection on interacting helical modes

The interplay between topology and interactions on the edge of a two dimensional topological insulator with time reversal symmetry is studied. We consider a simple non-interacting system of three helical channels with an inherent \(\mathbb{Z}_{2}\) topological protection, and hence a zero-temperature conductance of \(G=e^2/h\). We show that when interactions are added to the model, the ground state exhibits two different phases as function of the interaction parameters. One of these phases is a trivial insulator at zero temperature, as the symmetry protecting the non-interacting topological phase is spontaneously broken. In this phase, there is zero conductance \(G=0\) at zero-temperature. The other phase displays enhanced topological properties, with the neutral sector described by a massive version of \(\mathbb{Z}_{3}\) parafermions. In this phase, the system at low energies displays an emergent \(\mathbb{Z}_3\) symmetry, which is not present in the lattice model, and has a topologically protected zero-temperature conductance of \(G=3e^2/h\). This state is an example of a dynamically enhanced symmetry protected topological state.