Universality classes of the Anderson transitions driven by quasiperiodic potential in the three-dimensional Wigner-Dyson symmetry classes

A quasiperiodic system is an intermediate state between periodic and disordered systems with a unique delocalization-localization transition driven by the quasiperiodic potential (QP). One of the intriguing questions is whether the universality class of the Anderson transition (AT) driven by QP is similar to that of the AT driven by the random potential in the same symmetry class. Here, we study the critical behavior of the ATs driven by QP in the three-dimensional (3D) Anderson model, the Peierls phase model, and the Ando model, which belong to the Wigner-Dyson symmetry classes. The localization length and two-terminal conductance have been calculated using the transfer-matrix method, and we argue that their error estimations in statistics suffer from the correlation of QP. With the correlation under control, the critical exponents v of the ATs driven by QP are estimated by the finite-size scaling analysis of conductance, and they are consistent with the exponents v of the ATs driven by the random potential. Moreover, the critical conductance distribution and the level spacing ratio distribution have been studied. We also find that a convolutional neural network trained by the localized/delocalized wave functions in a disordered system predicts the localization/delocalization of the wave functions in quasiperiodic systems. Our numerical results strongly support the idea that the universality classes of the ATs driven by QP and the random potential are similar in the 3D Wigner-Dyson symmetry classes.

Automated summary

This study investigates the critical behavior of Anderson transitions driven by quasiperiodic potentials in the 3D Wigner-Dyson symmetry classes. By analyzing the conductance with finite-size scaling, the critical exponents are estimated and found to be consistent with those for Anderson transitions driven by random potentials. The critical conductance distribution and level spacing ratio distribution are also studied, and a convolutional neural network is found to accurately predict the localization/delocalization of wave functions in quasiperiodic systems.