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Quasiperiodic system is an intermediate state between periodic and disorderedsystems with unique delocalization-localization transition driven by thequasiperiodic potential (QP). One of the intriguing questions is whether theuniversality class of the Anderson transition (AT) driven by QP is similar tothat 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, Peierls phase model, and Ando model, which belong to theWigner-Dyson symmetry classes. The localization length and two-terminalconductance have been calculated by the transfer matrix method, and we arguethat their error estimations in statistics suffer from the correlation of QP.With the correlation under control, the critical exponents $\nu$ of the ATsdriven by QP are estimated by the finite size scaling analysis of conductance,which are consistent with $\nu$'s of the ATs driven by the random potential.Moreover, the critical conductance distribution and the level spacing ratiodistribution have been studied. We also find that a convolutional neuralnetwork trained by the localized/delocalized wavefunctions in a disorderedsystem predicts the localized/delocalized wavefunctions in quasiperiodicsystems. Our numerical results strongly support that the universality classesof the ATs driven by QP and random potential are similar in the 3D Wigner-Dysonsymmetry classes.

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