Anderson localization transitions in disordered non-Hermitian systems with exceptional points

Abstract

The critical exponents of continuous phase transitions of a Hermitian system depend on and only on its dimensionality and symmetries. This is the celebrated notion of the universality of continuous phase transitions. Here we numerically study the Anderson localization transitions in non-Hermitian two-dimensional (2D) systems with exceptional points by using the finite-size scaling analysis of the participation ratios. At the exceptional points of either second order or fourth order, two non-Hermitian systems with different symmetries have the same critical exponent $\ensuremath{\nu}\ensuremath{\simeq}2$ of correlation lengths, which differs from all known 2D disordered Hermitian and non-Hermitian systems. These feature is reminiscent of the superuniversality notion of Anderson localization transitions. In the symmetry-preserved and symmetry-broken phases, the non-Hermitian models with time-reversal symmetry and without spin-rotational symmetry, and without both time-reversal and spin-rotational symmetries, are in the same universality class of 2D Hermitian electron systems of Gaussian symplectic and unitary ensembles, where $\ensuremath{\nu}\ensuremath{\simeq}2.7$ and $\ensuremath{\nu}\ensuremath{\simeq}2.3$, respectively. The universality of the transition is further confirmed by showing that the critical exponent $\ensuremath{\nu}$ does not depend on the form of disorders and boundary conditions.