Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder

Abstract

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

4.1 pages (1 table and three figures) with supplemental materials

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• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Phase transitions in non-Hermitian superlattices
• Bichromatic state-dependent disordered potential for Anderson localization of ultracold atoms