Dual-mapping and quantum criticality in off-diagonal Aubry-Andr\'{e} models

We study a class of off-diagonal quasiperiodic hopping models described by one-dimensional SuSchrieffer-Heeger chain with quasiperiodic modulations. We unveil a general dual-mapping relation in parameter space of the dimerization strength λ and the quasiperiodic modulation strength V , regardless of the specific details of the quasiperiodic modulation. Moreover, we demonstrated semianalytically and numerically that under the specific quasiperiodic modulation, quantum criticality can emerge and persist in a wide parameter space. These unusual properties provides a distinctive paradigm compared with the diagonal quasiperiodic systems.