θ renormalization, electron–electron interactions and super universality in the quantum Hall regime

2005/02/20 by A. M. M. Pruisken, I. S. Burmistrov · 35 citations
Materials Science · Physics and Astronomy · #Electron #Functional renormalization group #Graphene research and applications #Instanton #Mathematical physics #Observable #Physics #Physics of Superconductivity and Magnetism #Quantum Hall effect #Quantum and electron transport phenomena #Quantum electrodynamics #Quantum field theory #Quantum mechanics #Renormalization #Renormalization group #Theoretical physics #Universality (dynamical systems) #cond-mat.mes-hall

paper · pdf · doi:10.1016/j.aop.2006.11.007

published in Annals of Physics 322(6), 1265-1334 (Elsevier BV) · ReVTeX, 38 pages, 9 figures

arxiv created 2005/02/20 · openalex publication_date 2007/01/16 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The renormalization theory of the quantum Hall effect relies primarily on the non-perturbative concept of theta renormalization by instantons. Within the generalized non-linear sigma model approach initiated by Finkelstein we obtain the physical observables of the interacting electron gas, formulate the general (topological) principles by which the Hall conductance is robustly quantized and derive - for the first time - explicit expressions for the non-perturbative (instanton) contributions to the renormalization group beta- and gamma- functions. Our results are in complete agreement with the recently proposed idea of super universality which says that the fundamental aspects of the quantum Hall effect are all generic features the instanton vacuum concept in asymptotically free field theory.

Citations

• Integer Quantum Hall Effect of Interacting Electrons: Dynamical Scaling and Critical Conductivity
• Electronic transport and the localization length in the quantum Hall effect
• General topological features and instanton vacuum in quantum Hall and spin liquids
• Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
• Universal scaling results for the plateau–insulator transition in the quantum Hall regime
• Percolation, quantum tunnelling and the integer Hall effect
• Non-Fermi-liquid theory for disordered metals near two dimensions
• (Mis-)handling gauge invariance in the theory of the quantum Hall effect. III. The instanton vacuum and chiral-edge physics