Universality classes of the Anderson transitions driven by quasiperiodic potential

Xunlong Luo, Tomi Ohtsuki

Published 2022-07-19Version 1

Quasiperiodic system is an intermediate state between periodic and disordered system with unique delocalization-localization transition driven by quasiperiodic potential (QP). One of the intriguing question is whether the universality class of the Anderson transition (AT) driven by QP is similar to that of the AT driven by 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 the Wigner-Dyson symmetry classes. The localization length and two terminal conductance have been calculated by the transfer matrix method, and we argue that their error estimation in statistics suffers from the correlation of QP. With the correlation under control, the critical exponents $\nu$ of the ATs driven by QP are estimated by the finite size scaling analysis of conductance, which are consistent with $\nu$'s of the ATs driven by random potential. Moreover, the critical conductance distribution and the level spacing ratio distribution have been studied. We also find that the convolutional neural network trained by the localized/delocalized wavefunction in disordered system predicts the localized/delocalized wavefunction in quasiperiodic system. Our numerical results strongly support that the universality classes of the ATs driven by QP and random potential are similar in the 3D Wigner-Dyson symmetry classes.