Phase diagram of a non-Abelian Aubry-André-Harper model withp-wave superfluidity

We study theoretically a one-dimensional quasiperiodic Fermi system with topological p-wave superfluidity, which can be deduced from a topologically nontrivial tight-binding model on the square lattice in a uniform magnetic field and subject to a non-Abelian gauge field. The system may be regarded as a non-Abelian generalization of the well-known Aubry-André-Harper model. We investigate its phase diagram as a function of the strength of the quasidisorder and the amplitude of the p-wave order parameter through a number of numerical investigations, including a multifractal analysis. There are four distinct phases separated by three critical lines, i.e., two phases with all extended wave functions [(I) and (IV)], a topologically trivial phase (II) with all localized wave functions, and a critical phase (III) with all multifractal wave functions. Phase (I) is related to phase (IV) by duality. It also seems to be related to phase (II) by duality. Our proposed phase diagram may be observable in current cold-atom experiments, in view of simulating non-Abelian gauge fields and topological insulators/superfluids with ultracold atoms.