Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems

Explore a comprehensive lecture on unifying Anderson transitions in Hermitian and non-Hermitian systems. Delve into the ubiquitous phenomenon of Anderson transitions in random systems, where waves undergo localization-delocalization transitions. Examine the classification of these transitions in Hermitian Hamiltonians using the 10-fold Altland-Zirnbauer symmetry classes. Investigate how non-Hermiticity expands these symmetry classes to 38-fold, leading to changes in critical behavior of Anderson transitions. Discover a proposed correspondence between universality classes of Anderson transitions in Hermitian and non-Hermitian systems, revealing identical critical exponents of length scales. Uncover the concept of superuniversality, where Anderson transitions in different symmetry classes of non-Hermitian systems share the same critical exponent. Compare known critical exponents for non-Hermitian systems with their Hermitian counterparts and analyze numerical estimates of critical exponents in various symmetry classes in two and three dimensions. Learn how this correspondence explains the similarity in critical exponents between the magnon-Hall effect and quantum Hall effect in Hermitian systems.