Fractional Topology in interacting 1D Superconductors
Résumé
We investigate the topological phases of two one-dimensional (1D) interacting superconducting wires, and propose topological invariants directly measurable from ground state correlation functions. These numbers 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 discovered in [1] 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 inter-wire hopping amplitude $t_{\bot}$ at length scales below $\sim 1/t_{\bot}$. A large inter-wire hopping amplitude results in the emergence of two integer topological phases hosting one edge mode per boundary, shared between both wires. At large interactions the two wires are described by Mott physics, with the $t_{\bot}$ hopping amplitude resulting in a paramagnetic order.