Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems

TL;DR

This paper establishes a correspondence between Anderson transitions in Hermitian and non-Hermitian systems, revealing superuniversality and enabling the estimation of critical exponents across different symmetry classes.

Contribution

It introduces a novel framework linking the universality classes of Anderson transitions in Hermitian and non-Hermitian systems, including new critical exponents for several symmetry classes.

Findings

Critical exponents in non-Hermitian systems match those in Hermitian systems with chiral symmetry.

Superuniversality: different symmetry classes share the same critical exponents.

Estimated critical exponents for multiple symmetry classes in 2D and 3D are consistent with the proposed correspondence.

Abstract

Non-Hermiticity enriches the 10-fold Altland-Zirnbauer symmetry class into the 38-fold symmetry class, where critical behavior of the Anderson transitions (ATs) has been extensively studied recently. Here, we propose a correspondence of the universality classes of the ATs between Hermitian and non-Hermitian systems. We illustrate that the critical exponents of the length scale in non-Hermitian systems coincide with the critical exponents in the corresponding Hermitian systems with additional chiral symmetry. A remarkable consequence of the correspondence is superuniversality, i.e., the ATs in some different symmetry classes of non-Hermitian systems are characterized by the same critical exponent. In addition to the comparisons between the known critical exponents for non-Hermitian systems and their Hermitian counterparts, we obtain the critical exponents in symmetry classes AI, AII, AII$^{\dagger}$, CII$^{\dagger}$, and DIII in two and three dimensions. Estimated critical exponents are consistent with the proposed correspondence. According to the correspondence, some of the exponents also give useful information of the unknown critical exponents in Hermitian systems, paving a way to study the ATs of Hermitian systems by the corresponding non-Hermitian systems.