Model for topological <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>p</mml:mi></mml:math>-wave superconducting wires with disorder and interactions

We present a comprehensive theoretical study of interacting and disordered topological phases of coupled Kitaev wires, which may support further realistic applications of Majorana fermions. We develop a variety of analytical, mathematical, and numerical methods for one- and two-coupled wires, associated with a topological marker accessible from real-space correlation functions on the wire(s). We verify the stability of the topological superconducting phase and quantify disorder effects close to the quantum phase transitions, e.g., through two-point correlation functions or using a renormalization group analysis of disorder. We show that the double critical Ising (DCI) phase---a fractional Majorana liquid characterized by a pair of half central charges and topological numbers---is stabilized by strong interactions against disorder, which respects the inversion symmetry between the wires (i.e., parity conservation on each wire). In the presence of an interwire hopping term, the DCI phase turns into a protected topological phase with a bulk gap. We study the localization physics developing along the critical line for weaker interactions.