Critical behaviors of Anderson transitions driven by non-Hermitian disorders

The interplay of non-Hermiticity and disorder plays an important role in condensed matter physics. The 10-fold way classification becomes further enriched into a 38-fold way according to recent studies [1]. Here, we report the universal critical behaviors of Anderson transitions driven by non-Hermitian disorders in three-dimensional (3D) Anderson model [2] and 3D U(1) model, that belong to 3D class AI† and 3D class A in the 38 classes respectively. Based on the finite-size scaling analyses, critical exponents are estimated as ν =0.99 ± 0.05 for the class AI†, ν = 1.09 ± 0.05 for the class A. We further studied spectral rigidity and level spacing distribution at the critical point. These critical behaviors strongly support that non-Hermiticity changes the universal class of the Anderson transition.[1] K. Kawabata,et al., PRX, 9, 041015 (2019). R. Hamazaki, et al., PRR, 2, 023286 (2020). [2] Y. Huang, and B. I. Shklovskii, PRB, 101, 014204 (2020), 102, 064212 (2020).