Critical exponent for the quantum spin Hall transition in Z_2 network model

TL;DR

This paper estimates the critical exponent for the quantum spin Hall transition, overcoming previous challenges by analyzing Lyapunov exponents, and finds it consistent with trivial symplectic systems.

Contribution

The study provides a precise estimation of the critical exponent for the quantum spin Hall transition using Lyapunov exponents, clarifying its universality class.

Findings

Critical exponent estimated as 2.73 ± 0.02

Critical exponent matches that of trivial symplectic systems

Method overcomes edge state complications in localized phase

Abstract

We have estimated the critical exponent describing the divergence of the localization length at the metal-quantum spin Hall insulator transition. The critical exponent for the metal-ordinary insulator transition in quantum spin Hall systems is known to be consistent with that of topologically trivial symplectic systems. However, the precise estimation of the critical exponent for the metal-quantum spin Hall insulator transition proved to be problematic because of the existence, in this case, of edge states in the localized phase. We have overcome this difficulty by analyzing the second smallest positive Lyapunov exponent instead of the smallest positive Lyapunov exponent. We find a value for the critical exponent $\nu=2.73 \pm 0.02$ that is consistent with that for topologically trivial symplectic systems.