  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.
