Unifying the Anderson Transitions in Hermitian and Non-Hermitian Systems

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${}^{†}$, CII${}^{†}$, 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.

4.3 pages, 1 figure, 1 tables with supplemental materials

References in corpus (15)

• Anderson Transitions
• Topological Origin of Non-Hermitian Skin Effects
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Critical exponent for the quantum Hall transition
• Non-Hermitian Topological Theory of Finite-Lifetime Quasiparticles: Prediction of Bulk Fermi Arc Due to Exceptional Point
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Transfer matrix study of the Anderson transition in non-Hermitian systems
• Spectral rigidity of non-Hermitian symmetric random matrices near Anderson transition
• Thermal metal-insulator transition in a helical topological superconductor
• Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI
• Quantum Multicriticality in Disordered Weyl Semimetal
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
• Critical Behaviors of Anderson Transitions in Three Dimensional Orthogonal Classes with Particle-hole Symmetries
• Scaling at chiral quantum critical points in two dimensions

Cited by in corpus (35)

• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Symmetry of Open Quantum Systems: Classification of Dissipative Quantum Chaos
• Non-Hermitian Topological Phases: Principles and Prospects
• Singular-Value Statistics of Non-Hermitian Random Matrices and Open Quantum Systems
• Level statistics of real eigenvalues in non-Hermitian systems
• Anderson localization transitions in disordered non-Hermitian systems with exceptional points
• Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices
• Universal non-Hermitian transport in disordered systems
• Damping transition in an open generalized Aubry-André-Harper model
• Anisotropic Topological Anderson Transitions in Chiral Symmetry Classes
• Quantum criticality in the disordered Aubry-André model
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Field theory of non-Hermitian disordered systems
• Metal-insulator transition in a 2D system of chiral unitary class
• Universal scaling of Green's functions in disordered non-Hermitian systems
• Kibble-Zurek scaling in one-dimensional localization transitions
• Stark localization near Aubry-André criticality
• Topological effect on the Anderson transition in chiral symmetry classes
• From scale-free to Anderson localization: a size-dependent transition
• Generalized multifractality in 2D disordered systems of chiral symmetry classes
• Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes
• Universal hard-edge statistics of non-Hermitian random matrices
• Berezinskii-Kosterlitz-Thouless localization-localization transitions in disordered two-dimensional quantized quadrupole insulators
• Characterizing phase transitions and criticality in non-Hermitian extensions of the XY model
• Localization transition in non-Hermitian systems depending on reciprocity and hopping asymmetry
• Chiral Hinge Transport in Disordered Non-Hermitian Second-Order Topological Insulators
• Non-Hermitian off-diagonal disordered optical lattices
• Interactions-disorder duality and critical phenomena in nodal semimetals, dilute gases and other systems
• Critical behavior of Anderson transitions in higher dimensional Bogoliubov-de Gennes symmetry classes
• Critical properties in the non-Hermitian Aubry-Andre-Stark model
• Effect of Uncorrelated On-site Scalar Potential and Mass Disorder on Transport of Two-Dimensional Dirac Fermions
• Theory of the Anderson transition in three-dimensional chiral symmetry classes: Connection to type-II superconductors
• Supermetal-insulator transition in a non-Hermitian network model
• Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI${}^{†}$ and AII${}^{†}$
• Localization with non-Hermitian off-diagonal disorder