Non-Abelian generalization of non-Hermitian quasicrystals: <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="script">PT</mml:mi></mml:math> -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 loss or nonreciprocal effects. In this work, we introduce non-Abelian generalization non-Hermitian quasicrystal, in which the interplay between effects quasiperiodic potentials create mobility edges rich among extended, critical localized phases. These generic features are demonstrated investigating three variants Aubry-Andr\'e-Harper model. A unified characterization is given to their spectrum, localization, entanglement properties. Our findings thus add new members family uncover physics that can be triggered systems.