Numerical Study of a Dual Representation of the Integer Quantum Hall Transition

TL;DR

This paper investigates the critical properties of the integer quantum Hall transition using a dual composite-fermion representation, revealing delocalized states at criticality and computing critical exponents consistent with established models.

Contribution

It introduces a dual composite-fermion approach to study the IQH transition, providing new insights and calculating critical exponents that align with existing theories.

Findings

Critical exponent ν = 2.56 ± 0.02

Multifractal exponent η = 0.51 ± 0.01

CF states are delocalized at all energies at criticality

Abstract

We study the critical properties of the non-interacting integer quantum Hall to insulator transition (IQHIT) in a "dual" composite-fermion (CF) representation. A key advantage of the CF representation over electron coordinates is that at criticality, $\textit{CF states are delocalized at all}$ energies. The CF approach thus enables us to study the transition from a new vantage point. Using a lattice representation of CF mean-field theory, we compute the critical and multifractal exponents of the IQHIT. We obtain $\nu = 2.56 \pm 0.02$ and $\eta = 0.51\pm 0.01$, both of which are consistent with the predictions of the Chalker-Coddington network model formulated in the electron representation.