Exact non-Hermitian mobility edges in one-dimensional quasicrystal lattice with exponentially decaying hopping and its dual lattice

We analytically determine the non-Hermitian mobility edges of a one-dimensional quasiperiodic lattice model with exponential decaying hopping and complex potentials as well its dual model, which is just generalization Ganeshan-Pixley-Das Sarma nonreciprocal nearest-neighboring hopping. The presence term destroys self-duality symmetry thus prevents us exploring localization-delocalization point through looking for self-dual points. Nevertheless, by applying Avila's global theory, Lyapunov exponent can be exactly derived, enables to get an analytical expression edge model. Consequently, original obtained using transformation, creates exact mappings between spectra wavefunctions these two models.