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 report the superuniversality notion of Anderson localization transitions in non-Hermitian two-dimensional (2D) systems with exceptional points in which the critical exponents do not depend on the symmetries. The Anderson localization transitions are numerically studied 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 $\nu \simeq 2$ of correlation lengths. This value differs from all known 2D disordered Hermitian and non-Hermitian systems. In the symmetry-preserved and symmetry-broken phases, the non-Hermitian models with time-reversal symmetry and without spin-rotational symmetry (without time-reversal and spin-rotational symmetries) are in the same universality class of 2D Hermitian electron systems of Gaussian symplectic (unitary) ensemble, where $\nu \simeq 2.7$ ($\nu \simeq 2.3$). The universality of the transition is further confirmed by showing that the critical exponent $\nu$ does not depend on the form of disorders and boundary conditions. Our results suggest that non-Hermitian systems of different symmetries around their exceptional points form a superuniversality class.

14 pages, 9 figures

References in corpus (11)

• Anderson Transitions
• The physics of exceptional points
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Localization in disordered superconducting wires with broken spin-rotation symmetry
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems
• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Hermitian chiral boundary states in non-Hermitian topological insulators
• Linear level repulsions near exceptional points of non-Hermitian systems

Cited by in corpus (11)

• Anomalous Skin Effects in Disordered Systems with a Single non-Hermitian Impurity
• Hybrid scaling properties of localization transition in a non-Hermitian disorder Aubry-André model
• From scale-free to Anderson localization: a size-dependent transition
• Non-Hermitian control of localization in mosaic photonic lattices
• Expedited thermalization dynamics in incommensurate systems
• Berezinskii-Kosterlitz-Thouless localization-localization transitions in disordered two-dimensional quantized quadrupole insulators
• Fate of pseudo mobility-edge and multiple states in non-Hermitian Wannier-Stark lattice
• Dissipation induced transition between delocalization and localization in the three-dimensional Anderson model
• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
• Localization of Lindbladian Fermions
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors