Exact mobility edges in the non-Hermitian t1-t2 model

Quantum localization in 1D non-Hermitian systems, especially the search for exact single-particle mobility edges, has attracted considerable interest recently. While much progress has been made, the available methods to determine the ME in such models are still limited. In this work we use a new method to find a new class of exact mobility edges in 1D non-Hermitian quasiperiodic models with parity-time ($\PT$) symmetry. We illustrate our method by studying a specific model. We first use our method to determine the energy-dependent mobility edge as well as the spectrum for localized eigenstates in this model. We then demonstrate that the metal-insulator transition must occur simultaneously with the spontaneous $\PT$-symmetry breaking transition in this model. Finally, we propose an experimental protocol based on a 1D photonic lattice to distinguish the extended and localized single-particle states in our model. The results in our work can be applied to studying other non-Hermitian quasiperiodic models.