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

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