Robust Universality of Non-Hermitian Anderson Transitions: From Dyson Singularity to Model-Independent Scaling

Abstract: We investigate the universality of Anderson localization transitions in one-dimensional non-Hermitian systems exhibiting the skin effect. By developing a numerically stable Log-Space Non-Hermitian Scaling (LNS) method, we overcome the severe floating-point overflow issues associated with the exponential growth of transmittance (T ~ exp(2 gamma L)), enabling precision finite-size scaling analysis up to system sizes of L = 1200. We probe the critical behavior across three distinct disorder landscapes: uniform diagonal, binary diagonal, and off-diagonal (random hopping) disorder. While the uniform model exhibits a standard mobility edge, the off-diagonal model reveals a Dyson-like singularity at the band center (E = 0), where the system resists localization even at strong disorder due to sublattice symmetry protection. However, upon symmetry breaking (E != 0), we demonstrate that all considered models, regardless of the disorder distribution (continuous vs. discrete) or Hamiltonian structure (site vs. bond randomness), belong to the same robust universality class. The critical exponents are determined as nu = 1.50 +/- 0.00 and beta ~ 0.65 through unambiguous data collapse, establishing a model-independent description of non-Hermitian localization transitions.