Anderson localization and multifractal spectrum at the transition point in a two-dimensional non-Hermitian AII† system

Abstract

The Anderson localization transition in a two-dimensional AII† system is studied by eigenvalue statistics and then confirmed by the multifractal analysis of the wave functions at the transition point. The system is modeled by a two-dimensional lattice structure with real-quaternion off-diagonal elements and complex on-site energies, whose real and imaginary parts are two independent random variables. Via finite-size scaling analysis of eigenvalue spacing ratios, we find the non-Hermiticity reduces the critical disorder and give an estimate of the critical exponent ν = 1.89, showing the system belongs to a new universal class other than the AII class and probably shares the same exponent with two-dimensional Hermitian DIII systems although they have different symmetries. The Anderson localization transition is further confirmed by checking the linearity in the parametric representation of the singularity strength and by checking the universality of the forms of the singularity spectra of different system sizes. The generalized dimensions are obtained as and .