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

arXiv comment14 pages, 5 figures. Edited section 3 and 6. Added more references

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Cited by in corpus (6)

• Numerical Study of a Dual Representation of the Integer Quantum Hall Transition
• Interaction effects on quantum Hall transitions: dynamical scaling laws and superuniversality
• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Composite Fermion Nonlinear Sigma Models
• 3D Network Model for Strong Topological Insulator Transitions
• Random Magnetic Field and the Dirac Fermi Surface