Large N spin quantum Hall effect

Details Large N spin quantum Hall effect Large N spin quantum Hall effect

2001-04-26

arxiv.org/abs/cond-mat/0104506v2

Nucl.Phys. B 612 (3) (2001) 291-312

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

29 pages; few references added, statement about the density of states improved; published version

Scientific paper

10.1016/S0550-3213(01)00352-2

We introduce a large N version of the spin quantum Hall transition problem. It is formulated as a problem of Dirac fermions coupled to disorder, whose Hamiltonian belong to the symmetry class C. The fermions carry spin degrees of freedom valued in the algebra sp(2N), the spin quantum Hall effect corresponding to N=1. Arguments based on renormalization group transformations as well as on a sigma model formulation, valid in the large N limit, indicate the existence of a crossover as N varies. Contrary to the N=1 case, the large N models are shown to lead to localized states at zero energy. We also present a sigma model analysis for the system of Dirac fermions coupled to only sp(2N) random gauge potentials, which reproduces known exact results.

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