Topological Phase Transitions in the Disordered Haldane Model

TL;DR

This paper studies how disorder affects topological phases in the Haldane model, revealing disorder-driven and mass-driven phase transitions with critical exponents similar to those in the IQHE, using numerical methods.

Contribution

It introduces a detailed numerical analysis of disorder-induced topological phase transitions in the Haldane model, connecting them to quantum Hall phenomena and revealing varying critical exponents.

Findings

Disorder-driven transitions align with IQHE plateau transitions.

Mass-driven transitions show a continuously varying correlation length exponent.

Chern marker fluctuations diverge with a power-law near transitions.

Abstract

We investigate the phases and phase transitions of the disordered Haldane model in the presence of on-site disorder. We use the real-space Chern marker and transfer matrices to extract critical exponents over a broad range of parameters. The disorder-driven transitions are consistent with the plateau transitions in the Integer Quantum Hall Effect (IQHE), in conformity with recent simulations of disordered Dirac fermions. Our numerical findings are compatible with an additional line of mass-driven transitions with a continuously varying correlation length exponent. The values interpolate between free Dirac fermions and the IQHE with increasing disorder strength. We also show that the fluctuations of the Chern marker exhibit a power-law divergence in the vicinity of both sets of transitions, yielding another varying exponent. We discuss the interpretation of these results.