The large N theory exactly reveals the quantum Hall effect and theta-renormalization

Details The large N theory exactly reveals the quantum Hall effect and theta-renormalization The large N theory exactly reveals the quantum Hall effect and theta-renormalization

2000-12-30

arxiv.org/abs/cond-mat/0101003v1

Phys.Rev.Lett. 505 (2003) 4432

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

35 pages, 9 figures

Scientific paper

We revisit the $\theta$ dependence in $CP^{N-1}$ model with large $N$. We study the consequences of a recently discovered new ingredient of the instanton vacuum, i.e. the massless chiral edge excitations. Contrary to the previous believes, our results demonstrate that the large $N$ expansion displays all the fundamental features of the quantum Hall effect. This includes the {\em robust} quantization of the Hall conductance, as well as the appearance of massless bulk excitations at $\theta = \pi$. We conclude that the quantum Hall effect is a generic feature of the instanton vacuum, i.e. for any number of field components and not just for the theory in the replica limit alone.

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