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• W2092045058 abstract "Generic classical electron motion in a strong perpendicular magnetic field and random potential reduces to the bond percolation on a square lattice. Here we point out that for certain smooth two-dimensional potentials with $120ifmmode^circelsetextdegreefi{}$ rotational symmetry this problem reduces to the site percolation on a triangular lattice. We use this observation to develop an approximate analytical description of the integer quantum Hall transition. For this purpose we devise a quantum generalization of the real-space renormalization group (RG) treatment of the site percolation on the triangular lattice. In quantum case, the RG transformation describes the evolution of the distribution of the $3ifmmodetimeselsetexttimesfi{}3$ scattering matrices at the sites. We find the fixed point of this distribution and use it to determine the critical exponent, $ensuremath{nu}$, for which we find the value $ensuremath{nu}ensuremath{approx}2.3textdiv{}2.76$. The RG step involves only a single Hikami box and thus can serve as a minimal RG description of the quantum Hall transition." @default.
• W2092045058 created "2016-06-24" @default.
• W2092045058 creator A5040301901 @default.
• W2092045058 creator A5058428152 @default.
• W2092045058 date "2009-03-03" @default.
• W2092045058 modified "2023-10-16" @default.
• W2092045058 title "Quantum site percolation on triangular lattice and the integer quantum Hall effect" @default.
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• W2092045058 doi "https://doi.org/10.1103/physrevb.79.125401" @default.
• W2092045058 hasPublicationYear "2009" @default.
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