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 noninteracting system of three helical channels with an inherent

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 a function of the interaction parameters. One of these phases is a trivial insulator at zero temperature, as the symmetry protecting the noninteracting 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 a topologically protected zero-temperature conductance of G=3e^2/h and an emergent Z_3 symmetry not present in the lattice model. The neutral sector in this phase is described by a massive version of Z_3

parafermions. This state is an example of a dynamically enhanced symmetry-protected topological state.