Quantum Critical Exponents for a Disordered Three-Dimensional Weyl Node

TL;DR

This paper precisely determines the critical exponents for a disorder-driven quantum phase transition in three-dimensional Weyl semimetals using numerical simulations, challenging previous theoretical and numerical estimates.

Contribution

It provides the first high-precision numerical estimates of the critical exponents $ u$ and $z$ for the disorder-induced transition in Weyl semimetals, using a minimal model and finite-size scaling.

Findings

Critical exponent $ u=1.47\u00b10.03$

Dynamical exponent $z=1.49\u00b10.02$

Results are incompatible with previous studies

Abstract

Three-dimensional Dirac and Weyl semimetals exhibit a disorder-induced quantum phase transition between a semimetallic phase at weak disorder and a diffusive-metallic phase at strong disorder. Despite considerable effort, both numerically and analytically, the critical exponents $\nu$ and $z$ of this phase transition are not known precisely. Here we report a numerical calculation of the critical exponent $\nu=1.47\pm0.03$ using a minimal single-Weyl node model and a finite-size scaling analysis of conductance. Our high-precision numerical value for $\nu$ is incompatible with previous numerical studies on tight-binding models and with one- and two-loop calculations in an $\epsilon$-expansion scheme. We further obtain $z=1.49\pm0.02$ from the scaling of the conductivity with chemical potential.