  We study the topology and localization properties of a generalized
Su-Schrieffer-Heeger (SSH) model with a quasi-periodic modulated hopping. It is
found that the interplay of off-diagonal quasi-periodic modulations can induce
topological Anderson insulator (TAI) phases and reentrant topological Anderson
insulator (RTAI), and the topological phase boundaries can be uncovered by the
divergence of the localization length of the zero-energy mode. In contrast to
the conventional case that the TAI regime emerges in a finite range with the
increase of disorder, the TAI and RTAI are robust against arbitrary modulation
amplitude for our system. Furthermore, we find that the TAI and RTAI can induce
the emergence of reentrant localization transitions. Such an interesting
connection between the reentrant localization transition and the TAI/RTAI can
be detected from the wave-packet dynamics in cold atom systems by adopting the
technique of momentum-lattice engineering.
