Localization properties of random-mass Dirac fermions from real-space renormalization group

TL;DR

This paper investigates the localization and phase transitions of random-mass Dirac fermions using real-space renormalization group methods, revealing detailed phase behavior and resonance-driven delocalization mechanisms.

Contribution

It provides a simple RG framework that accurately describes phases and transitions in the Cho-Fisher model of Dirac fermions with mass disorder.

Findings

Identifies three phases: thermal metal and two insulators with quantized Hall conductance.

Shows delocalization driven by proliferation of perfect resonances.

Demonstrates synchronization of conductance distribution evolution with sign percolation.

Abstract

Localization properties of random-mass Dirac fermions for a realization of mass disorder, commonly referred to as Cho-Fisher model, is studied on the D-class chiral network. We show that a simple RG description captures accurately three phases: thermal metal and two insulators with quantized Hall conductances, as well as transitions between them (including critical exponents). We find that, with no randomness in phases on the links, transmission via the RG block exhibits a sizable portion of perfect resonances. Delocalization occurs by proliferation of these resonances to larger scales. Evolution of the thermal conductance distribution towards metallic fixed point is synchronized with evolution of signs of transmission coefficients, so that delocalization is accompanied with sign percolation