Exact mobility edges for 1D quasiperiodic models

Mobility edges (ME), i.e. critical energies which separate absolutely continuous spectrum and purely point spectrum, is an important issue in quantum physics. So far there are two experimentally feasible 1D quasiperiodic models that have been discovered to have exact mobility edge. However, all the theoretical studies have remained at the numerical level. In this paper, we rigorously prove the existence and give the precise location of the MEs for these models.