Emergent Non-Abelian Thouless Pumping Induced by the Quasiperiodic Disorder

Abstract: We investigate the non-Abelian Thouless pumping in a disorder tunable Lieb chain with degenerate flat bands. The results reveal that quasiperiodic disorder will cause a topological phase transition from the trivial (without non-Abelian Thouless pumping) to the non-trivial (with non-Abelian Thouless pumping) phase. The mechanism behind is that the monopole originally outside the topological region can be driven into the topological region due to the introduction of quasiperiodic disorder. Moreover, since the corresponding monopole will turn into a nodal line to spread beyond the boundaries of the topological region, the system with large disorder strength will result in the disappearance of non-Abelian Thouless pumping. Furthermore, we numerically simulate the Thouless pumping of non-Abelian systems, and the evolution results of center of mass' displacement are consistent with the Chern number. Finally, we discuss the localization properties of the system and find that, similar to [PRL 130, 206401(2023)], the inverse Anderson transition does not occur in the system with the increase of quasiperiodic strength, while the system still maintains the coexistence of localized and extended states.