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

TL;DR

This study investigates whether the Anderson transition driven by quasiperiodic potentials shares the same universality class as that driven by random potentials in three-dimensional Wigner-Dyson symmetry classes, using numerical analysis and neural networks.

Contribution

It provides numerical evidence that the universality classes of Anderson transitions driven by quasiperiodic and random potentials are similar in 3D Wigner-Dyson classes.

Findings

Critical exponents are consistent between quasiperiodic and random potential-driven transitions.

Critical conductance distribution and level spacing ratios are similar in both cases.

Neural networks trained on disordered systems can predict wavefunctions in quasiperiodic systems.

Abstract

Quasiperiodic system is an intermediate state between periodic and disordered systems with 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, 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 estimations in statistics suffer 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 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 wavefunctions in a disordered system predicts the localized/delocalized wavefunctions in quasiperiodic systems. 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.