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

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.

13 pages, 8 figures, 1 table

References in corpus (16)

• Anderson Transitions
• Localization of interacting fermions at high temperature
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Photonic topological pumping through the edges of a dynamical four-dimensional quantum Hall system
• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Observation of Topological Phase Transitions in Photonic Quasicrystals
• Deep Learning the Quantum Phase Transitions in Random Two-Dimensional Electron Systems
• Anderson transition in three-dimensional systems with non-Hermitian disorder
• Universality classes of the Anderson Transitions Driven by non-Hermitian Disorder
• Anderson localization transitions with and without random potentials
• Deep Learning the Quantum Phase Transitions in Random Electron Systems: Applications to Three Dimensions
• Phase Diagrams of Three-Dimensional Anderson and Quantum Percolation Models using Deep Three-Dimensional Convolutional Neural Network
• Quantum Multicriticality in Disordered Weyl Semimetal
• Estimate of the critical exponent of the Anderson transition in the three and four dimensional unitary universality classes
• Delocalization and scaling properties of low-dimensional quasiperiodic systems
• The GOE ensemble for quasiperiodic tilings without unfolding: $r$-value statistics