# Self-duality of the integer quantum Hall to insulator transition: composite fermion description

## TL;DR

This paper demonstrates the self-duality of the integer quantum Hall to insulator transition using a composite fermion framework, revealing a critical resistivity tensor consistent with theoretical and experimental expectations.

## Contribution

It provides an explicit analytical proof of self-duality at the transition via electron and composite fermion Lagrangians and non-linear sigma models.

## Key findings

- Resistivity tensor at criticality: ρ_xx = ρ_xy = h/e^2
- Self-duality is shown through equivalence of electron and CF descriptions
- Analytical results align with experimental observations

## Abstract

The integer quantum Hall to insulator transition (IQHIT) is a paradigmatic quantum critical point. Key aspects of this transition, however, remain mysterious, due to the simultaneous effects of quenched disorder and strong interactions. We study this transition using a composite fermion (CF) representation, which incorporates some of the effects of interactions. As we describe, the transition also marks a IQHIT of CFs: this suggests that the transition may exhibit `self-duality'. We show the explicit equivalence of the electron and CF Lagrangians at the critical point via the corresponding non-linear sigma models, revealing the self-dual nature of the transition. We show analytically that the resistivity tensor at the critical point is $\rho^c_{xx} = \rho^c_{xy} = \frac{h}{e^2}$, which are consistent with the expectations of self-duality, and in rough agreement with experiments.