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

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 $$\rho^c_{xx} = \rho^c_{xy} = \frac{h}{e<sup>2}$$, which are consistent with the expectations of self-duality, and in rough agreement with experiments.