  A mobility edge (ME) in energy separating extended from localized states is a
central concept in understanding various fundamental phenomena like the
metal-insulator transition in disordered systems. In one-dimensional
quasiperiodic systems, there exist a few models with exact MEs, and these
models are beneficial to provide exact understanding of ME physics. Here we
investigate two widely studied models including exact MEs, one with an
exponential hopping and one with a special form of incommensurate on-site
potential. We analytically prove that the two models are mutually dual, and
further give the numerical verification by calculating the inverse
participation ratio and Husimi function. The exact MEs of the two models are
also obtained by calculating the localization lengths and using the duality
relations. Our result may provide insight into realizing and observing exact
MEs in both theory and experiment.
