Non-perturbative Solution of the Unitary, $N$-Orbital Anderson Model

Details Non-perturbative Solution of the Unitary, $N$-Orbital Anderson Model Non-perturbative Solution of the Unitary, $N$-Orbital Anderson Model

2011-09-21

arxiv.org/abs/1109.4539v2

Physics

Condensed Matter

Disordered Systems and Neural Networks

4 pages, revtex. Discussion of spatial uniformity approximation of Q included. References added, typos/errors corrected. Inclu

Scientific paper

The exact Anderson transition point is extracted from a non-perturbative analysis of an $N$-orbital model of electrons with broken time-reversal invariance moving in random potential. Neglecting spatial fluctuations of the matrix field, the functional integral of F. Wegner's real matrix ensemble (RME) replica field theory is reformulated in terms of a partition function of a classical Coulomb gas and evaluated in the replica limit $n\to0$, as a random matrix average. At large $N$, the zero frequency susceptibility diverges like $\chi\sim |\omega|^{-\gamma}$ with critical exponent $\gamma=1/2$. Furthermore, by including a topological term, the analysis may provide a route towards a precise solution of the integer quantum Hall plateau transition.

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