Effect of Topology on the Anderson Transitions in Non-Hermitian Systems

Using Hermitization, we have proven that critical exponents of the length scale in non-Hermitian systems coincide with the critical exponents in the corresponding Hermitian systems [1]. The correspondence enables us to evaluate critical exponents in Hermitian systems with larger system sizes. Several tight-binding models in non-Hermitian symmetry classes A and AI are studied by transfer matrix method. Accurate critical exponents are obtained and compared with known results in corresponding Hermitian symmetry classes AIII and BDI [2][3]. Based on the numerical results, we propose a topological mechanism that explains a variance of critical exponents in the same Hermitian symmetry class.