Unconventional scaling theory in disorder-driven quantum phase transition

Abstract

We clarify novel forms of scaling functions of conductance, critical conductance distribution and localization length in a disorder-driven quantum phase transition between band insulator and Weyl semimetal phases. Quantum criticality of the phase transition is controlled by a clean-limit fixed point with spatially anisotropic scale invariance. We argue that the anisotropic scale invariance is reflected on unconventional scaling function forms in the quantum phase transition. We verify the proposed scaling function forms in terms of transfer-matrix calculations of conductance and localization length in a tight-binding model.

arXiv comment4 pages with supplemental materials

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• Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
• Rare regions and avoided quantum criticality in disordered Weyl semimetals and superconductors
• Critical Behaviors of Anderson Transitions in Three Dimensional Orthogonal Classes with Particle-hole Symmetries
• Ballistic transport in disordered Dirac and Weyl semimetals
• Renormalization group analysis of Dirac fermions with random mass
• Global phase diagram of Coulomb-interacting anisotropic Weyl semimetals with disorder