Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2005-02-20
Annals Phys. (N.Y.) 322 (2007) 1265
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
ReVTeX, 38 pages, 9 figures
Scientific paper
10.1016/j.aop.2006.11.007
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.
Burmistrov Igor S.
Pruisken A. M. M.
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