Interplay of topological superconductivity and interactions at the edge of topological insulators: a DMRG perspective*

It was proposed that the edge states of two dimensional topological insulators in the presence of superconductivity and magnetic domains host zero energy Majorana bound states at the domain boundaries. A pair of domain walls host a pair of Majorana fermions, leading to a twofold degenerate ground state. This degeneracy, in turn, can be used to define a highly non-local qubit that is resilient to local perturbations. However, time reversal symmetry in these systems is explicitly broken by the external magnetic field. Another way to gap the edge modes, without breaking this symmetry explicitly, can be achieved by interactions. Based on low energy bosonized calculations, there are also zero energy bound states expected to be localized at domain walls between interacting and superconducting regions. Due to the time reversal symmetry, a fourfold degenerate ground state is expected, which exhibit a richer phase diagram due to the interplay of interactions and topological superconductivity. 

In the present work we devise a simple model which is capable to encode key features of the edge states of topological insulators and arbitrary strong interactions in the presence of superconductivity. Utilizing density matrix renormalization group calculations we explore the phase diagram in terms of interactions preserving time reversal symmetry. We identify parameter ranges where a system can host topological interface states and characterize these through the Josephson current.