Universality Classes of the Anderson Transitions Driven by Non-Hermitian Disorder

The interplay between non-Hermiticity and disorder plays an important role in condensed matter physics. Here, we report the universal critical behaviors of Anderson transitions driven by non-Hermitian disorders for a three-dimensional (3D) model 3D U(1) model, which belong to class ${\mathrm{AI}}^{\ifmmode\dagger\else\textdagger\fi{}}$ A classification systems, respectively. Based on level statistics finite-size scaling analysis, exponent length scale is estimated as $\ensuremath{\nu}=0.99\ifmmode\pm\else\textpm\fi{}0.05$ ${\mathrm{AI}}^{\ifmmode\dagger\else\textdagger\fi{}}$, $\ensuremath{\nu}=1.09\ifmmode\pm\else\textpm\fi{}0.05$ A, both are clearly distinct from exponents orthogonal unitary classes, In addition, spectral rigidity, spacing distribution, ratio distribution studied. These strongly support that changes universality classes transitions.