Fractional topology in interacting one-dimensional superconductors

We investigate the topological phases of two one-dimensional (1D) interacting superconducting wires and pro-pose topological markers directly measurable from ground-state correlation functions. These quantities remain powerful tools in the presence of couplings and interactions. We show with the density matrix renormalization group that the double critical Ising (DCI) phase of two interacting Kitaev chains is a fractional topological phase with gapless Majorana modes in the bulk, and a one-half topological invariant per wire. Using both numerics and quantum field theoretical methods, we show that the phase diagram remains stable in the presence of an interwire hopping amplitude t perpendicular to at length scales below similar to 1/t perpendicular to. A large interwire hopping amplitude results in the emergence of two integer topological phases, stable also at large interactions. They host one edge mode per boundary shared between both wires. At large interactions, the two wires are described by Mott physics, with the t perpendicular to hopping amplitude resulting in a paramagnetic order.