Universality Classes of Anderson Transition in Non-Standard Symmetry Classes

Disorder-driven quantum phase transitions in Hermitian chiral symmetry classes share same universality classes with non-Hermitian systems in their fundamental symmetry classes [1]. We study the criticality of the Anderson transition of three-dimensional (3D) disordered systems in the chiral symplectic class (CII), and show that the critical exponent of localization length of a Class CII model is quite close to that of a Class D model [2]. To investigate a possible superuniversality between the two Hermitian classes, we compare other universal critical quantities at the transition point in the two 3D models. We will also show an effect of one-dimensional (1D) weak topology in the Class CII model, and discuss an emergence of quasi-localization phenomena [2,3] in the chiral symplectic class.

[1] X. Luo, Z. Xiao, K. Kawabata, T. Ohtsuki, and R. Shindou, Phys. Rev. Research, 4 L022035 (2022).

[2] T. Wang, T. Ohtsuki, and R. Shindou, Phys. Rev. B 104, 014206 (2021).

[3] Z. Xiao, K. Kawabata, X. Luo, T. Ohtsuki, and R. Shindou, Phys. Rev. Lett. 131 056301 (2023).

[4] P. Zhao, Z. Xiao, Y. Zhang, and R. Shindou, arXiv2402.02310, to appear in Phys. Rev. Lett.