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We study a one-dimensional lattice model subject to non-Hermitianquasiperiodic potentials. Firstly, we strictly demonstrate that there exists aninteresting dual mapping relation between $|a|<1$ and $|a|>1$ with regard tothe potential tuning parameter $a$. The localization property of $|a|<1$ can bedirectly mapping to that of $|a|>1$, the analytical expression of the mobilityedge of $|a|>1$ is therefore obtained through spectral properties of $|a|<1$.More impressive, we prove rigorously that even if the phase $\theta \neq 0$ inquasiperiodic potentials, the model becomes non-$\mathcal{PT}$ symmetric,however, there still exists a new type of real-complex transition driven bynon-Hermitian disorder, which is a new universality class beyond $\mathcal{PT}$symmetric class.

Real-complex transition driven by quasiperiodicity: a new universality class beyond $\mathcal{PT}$ symmetric one