Real-complex transition driven by quasiperiodicity: A class of non- PT symmetric models

Abstract

We study a one-dimensional lattice model subject to non-Hermitian quasiperiodic potentials. First, we strictly demonstrate that there exists an interesting dual mapping relation between $|a|<1$ and $|a|>1$ with regard to the potential tuning parameter $a$. The localization property of $|a|<1$ can be directly mapped to that of $|a|>1$, the analytical expression of the mobility edge of $|a|>1$ is therefore obtained through the spectral properties of $|a|<1$. More impressive, we prove rigorously that, even if the phase $\ensuremath{\theta}\ensuremath{\ne}0$ in quasiperiodic potentials, the model becomes non-$\mathcal{PT}$ symmetric, however, there still exists a type of real-complex transition driven by non-Hermitian disorder, which is a class beyond the $\mathcal{PT}$-symmetric class.