Fractional topology in interacting one-dimensional superconductors

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