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

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 CI). first introduce tight-binding models on cubic lattice that belong to these five nonstandard symmetry respectively. Unlike the Bogoliubov-de Gennes Hamiltonian for superconductors, all have finite areas Fermi surfaces momentum space clean limit. Thereby, scaling theory Anderson transition guarantees presence at disorder strength models. Based this expectation, we carry out extensive transfer matrix calculations Lyapunov exponents zero-energy eigenstates disordered quasi-one-dimensional geometry. Near point, correlation length diverges a exponent $\nu$. Using finite-size analysis localization length, determine function (normalized) three non-standard classes: $\nu_{\text{AIII}}=1.06\pm0.02$, $\nu_{\text{D}}=0.87\pm0.03$, $\nu_{\text{C}}=0.996\pm0.012$. Our result class is consistent previous study classical network model [M. Ortu\~no et al, Phys. Rev. Lett. 102, 070603 (2009)]. The two are estimated as $\nu_{\text{CI}}=1.17 \pm 0.02$ $\nu_{\text{BDI}}=1.12 0.06$. CI another model, while BDI variance evaluation nodal Dirac ring [X. L. Luo B. 101, 020202(R) (2020)].