Phase diagram of a non-Abelian Aubry-Andr\'e-Harper model with $p$-wave superfluidity

TL;DR

This paper explores the phase diagram of a non-Abelian Aubry-Andre9-Harper model with p-wave superfluidity, revealing four distinct phases with different wave-function characteristics, relevant for cold-atom experimental simulations.

Contribution

It introduces a non-Abelian generalization of the Aubry-Andre9-Harper model with topological p-wave superfluidity and maps its phase diagram using numerical and multifractal analyses.

Findings

Identifies four distinct phases with extended, localized, and multifractal wave-functions.

Discovers duality relations between phases I and IV, and I and II.

Provides a phase diagram potentially observable in cold-atom experiments.

Abstract

We theoretically study a one-dimensional quasi-periodic Fermi system with topological $p$-wave superfluidity, which can be deduced from a topologically non-trivial 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 a non-Abelian generalization of the well-known Aubry-Andr\'e-Harper model. We investigate its phase diagram as functions of the strength of the quasi-disorder 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. The phase I is related to the phase IV by duality. It also seems to be related to the 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.