Ising anyonic topological phase of interacting fermions in one dimension

We study a microscopic model of interacting fermions in a ladder setup, where the total number of particles is conserved. At a special point, the ground state is known and gives rise to a topological state of matter with edge modes obeying the statistics of Ising anyons. Using a combination of bosonization as well as full scale numerical density-matrix renormalization group analysis, we map out the full phase diagram. We find that the topological phase survives in an extended parameter regime. Remarkably, an additional symmetry is required to protect the topological phase.