Universality classes of the Anderson transition in three-dimensional symmetry classes AIII, BDI, C, D and CI

Abstract

We clarify universal critical properties of delocalization-localization transitions in three-dimensional (3D) unitary and orthogonal classes with particle-hole and/or chiral symmetries (classes AIII, BDI, D, C and CI). We first introduce tight-binding models on cubic lattice that belong to these five nonstandard symmetry classes respectively. Unlike the Bogoliubov-de Gennes Hamiltonian for superconductors, all the five models have finite areas of Fermi surfaces in the momentum space in the clean limit. Thereby, the scaling theory of the Anderson transition guarantees the presence of the delocalization-localization transitions at finite disorder strength in these models. Based on this expectation, we carry out extensive transfer matrix calculations of the Lyapunov exponents for zero-energy eigenstates of the disordered tight-binding models with quasi-one-dimensional geometry. Near the Anderson transition point, the correlation length diverges with a universal critical exponent $\nu$. Using finite-size scaling analysis of the localization length, we determine the critical exponent of the transitions and scaling function of the (normalized) localization length in the three non-standard unitary symmetry classes: ${\nu }_{\text{AIII}}=1.06\pm 0.02$, ${\nu }_{\text{D}}=0.87\pm 0.03$, and ${\nu }_{\text{C}}=0.996\pm 0.012$. Our result of the class C is consistent with a previous study of classical network model [M. Ortuño et al, Phys. Rev. Lett. 102, 070603 (2009)]. The critical exponents of the two non-standard orthogonal classes are estimated as ${\nu }_{\text{CI}}=1.17\pm 0.02$ and ${\nu }_{\text{BDI}}=1.12\pm 0.06$. Our result of the class CI is consistent with another previous study of a lattice model, while the exponent of the class BDI is at variance with the previous evaluation of nodal Dirac ring model [X. L. Luo et al, Phys. Rev. B. 101, 020202(R) (2020)].

arXiv comment11 pages, 3 figures, 2 tables

References in corpus (46)

• Classification of topological insulators and superconductors in three spatial dimensions
• Many body localization and thermalization in quantum statistical mechanics
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Weyl Semimetal in a Topological Insulator Multilayer
• Anderson Transitions
• Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Time-Reversal Symmetry Breaking Superconductivity in Sr2RuO4
• Localization of ultrasound in a three-dimensional elastic network
• Many-body localization in a disordered quantum Ising chain
• High Resolution Polar Kerr Effect Measurements of Sr2RuO4: Evidence for Broken Time Reversal Symmetry in the Superconducting State
• Spectral Density of the QCD Dirac Operator near Zero Virtuality
• Corrections to scaling at the Anderson transition
• Topological Criticality in the Chiral-Symmetric AIII Class at Strong Disorder
• Observation of broken time-reversal symmetry in the heavy fermion superconductor UPt${}_3$
• Anderson localization in Bose-Einstein condensates
• Transport Phase Diagram and Anderson Localization in Hyperuniform Disordered Photonic Materials
• Symmetry classes of disordered fermions
• Critical exponent for the Anderson transition in the three dimensional orthogonal universality class
• Non-Hermitian disorder in two-dimensional optical lattices
• Nonunitary Scaling Theory of Non-Hermitian Localization
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Effect of Disorder in a Three-Dimensional Layered Chern Insulator
• AIII and BDI Topological Systems at Strong Disorder
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Random matrix theory and $QC{D}_3$
• Magnetic-field-driven localization of light in a cold-atom gas
• Disorder-induced trapping versus Anderson localization in Bose-Einstein condensates expanding in disordered potentials
• Metal-insulator transition in 2D random fermion systems of chiral symmetry classes
• Universality and the QCD Anderson Transition
• Critical Exponent of the Anderson Transition using Massively Parallel Supercomputing
• Integer Quantum Magnon Hall Plateau-Plateau Transition in a Spin Ice Model
• Spectral rigidity of non-Hermitian symmetric random matrices near Anderson transition
• Light Localization and Cooperative Coupling Effects in Aperiodic Vogel Spirals
• Finite-size scaling analysis of localization transition for scalar waves in a 3D ensemble of resonant point scatterers
• Anderson transition and multifractals in the spectrum of the Dirac operator of Quantum Chromodynamics at high temperature
• Global phase diagram of a three dimensional dirty topological superconductor
• Level statistics of extended states in random non-Hermitian Hamiltonians
• Localization transition for light scattering by cold atoms in an external magnetic field
• Anderson transition in the three dimensional symplectic universality class
• Random Walks and Anderson Localisation in a Three-Dimensional Class C Network Model
• Disorder driven phase transitions in weak AIII topological insulators
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
• Spectrum-wide quantum criticality at the surface of class AIII topological phases: An "energy stack" of integer quantum Hall plateau transitions
• Critical Behaviors of Anderson Transitions in Three Dimensional Orthogonal Classes with Particle-hole Symmetries
• Quantum Hall effects in layered disordered superconductors

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• Non-equilibrium dynamics of localization phase transition in the non-Hermitian Disorder-Aubry-André model
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