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Exact Mobility edges and topological Anderson insulating phase in a slowly varying quasiperiodic model

We uncover the relationship of topology and disorder in a one-dimensional Su-Schrieffer-Heeger chain subjected to a slowly varying quasi-periodic modulation. By numerically calculating the disorder-averaged winding number and analytically studying the localization length of the zero modes, we obtain the topological phase diagram, which implies that the topological Anderson insulator (TAI) can be induced by a slowly varying quasi-periodic modulation. Moreover, unlike the localization properties in the TAI phase caused by random disorder, mobility edges can enter into the TAI region identified by the fractal dimension, the inverse participation ratio, and the spatial distributions of the wave functions, the boundaries of which coincide with our analytical results.