Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry

We investigate the localization-delocalization transition in one-dimensional non-Hermitian quasiperiodic lattices with exponential short-range hopping, which possess parity-time (PT) symmetry. The localization transition induced by the non-Hermitian quasiperiodic potential is found to occur at the PT-symmetry-breaking point. Our results also demonstrate the existence of energy-dependent mobility edges, which separate the extended states from localized states and are only associated with the real part of eigenenergies. The level statistics and Loschmidt echo dynamics are also studied.