Theta renormalization, electron-electron interactions and super universality in the quantum Hall regime

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.

ReVTeX, 38 pages, 9 figures

References in corpus (2)

• The instanton vacuum of generalized $C{P}^{N-1}$ models
• General topological features and instanton vacuum in quantum Hall and spin liquids

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• Interaction and disorder effects in 3D topological insulator thin films
• Multifractality and electron-electron interaction at Anderson transitions
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• Spin-valley interplay in two-dimensional disordered electron liquid
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• The problem of "macroscopic charge quantization" in single-electron devices
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• Anyon superconductivity and plateau transitions in doped fractional quantum anomalous Hall insulators
• Exact Haldane mapping for all $S$ and super universality in spin chains
• Instanton analysis for the spin quantum Hall symmetry class: Non-perturbative corrections to physical observables and generalized multifractal spectrum
• Super universality of dimerised $SU(N+M)$ spin chains
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