2019/07/31 by Prashant Kumar, Yong Baek Kim, S. Raghu · 8 citations
Mathematics · Physics and Astronomy · #Atomic and Subatomic Physics Research #Composite fermion #Condensed matter physics #Critical point (mathematics) #Duality (order theory) #Electron #Fermion #Mathematical analysis #Mathematical physics #Mathematics #Physics #Physics of Superconductivity and Magnetism #Pure mathematics #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum critical point #Quantum mechanics #Quantum phase transition #Quantum spin Hall effect #Transition point #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.100.235124
published in Physical review. B./Physical review. B 100(23) (American Physical Society) · 14 pages, 5 figures. Edited section 3 and 6. Added more references
openalex created_date 2019/08/13 · arxiv created 2019/12/10 · openalex publication_date 2019/12/16 · arxiv updated 2019/12/25 · openalex updated_date 2026/08/05
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 an 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 nonlinear sigma models, revealing the self-dual nature of the transition. We show analytically that the resistivity tensor at the critical point is \ensuremathρxxc=\ensuremathρxyc=\frache2, which are consistent with the expectations of self-duality, and in rough agreement with experiments.