Non-Abelian generalization of non-Hermitian quasicrystals: PT-symmetry breaking, localization, entanglement, and topological transitions

Non-Hermitian quasicrystal forms a unique class of matter with symmetry-breaking, localization and topological transitions induced by gain and loss or nonreciprocal effects. In this work, we introduce a non-Abelian generalization of non-Hermitian quasicrystal, in which the interplay between non-Hermitian effects and non-Abelian quasiperiodic potentials create mobility edges and rich transitions among extended, critical and localized phases. These generic features are demonstrated by investigating three non-Abelian variants of the non-Hermitian Aubry-Andr\'e-Harper model. A unified characterization is given to their spectrum, localization, entanglement and topological properties. Our findings thus add new members to the family of non-Hermitian quasicrystal and uncover unique physics that can be triggered by non-Abelian effects in non-Hermitian systems.