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

TL;DR

This paper develops a non-perturbative renormalization framework for the quantum Hall effect using instantons within a non-linear sigma model, confirming the super universality hypothesis of the effect's fundamental features.

Contribution

It provides explicit formulas for instanton contributions to renormalization group functions and demonstrates the robustness of Hall conductance quantization in an interacting electron system.

Findings

Explicit instanton contributions to beta and gamma functions derived.

Hall conductance quantization shown to be topologically robust.

Results support the super universality hypothesis in quantum Hall physics.

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.