Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2000-02-14
Phys. Rev. B 62, 2008 (2000)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
9 pages, submitted to PRB
Scientific paper
10.1103/PhysRevB.62.2008
We present a novel approach to the localization-delocalization transition in the integer quantum Hall effect. The Hamiltonian projected onto the lowest Landau level can be written in terms of the projected density operators alone. This and the closed set of commutation relations between the projected densities leads to simple equations for the time evolution of the density operators. These equations can be used to map the problem of calculating the disorder averaged and energetically unconstrained density-density correlation function to the problem of calculating the one-particle density of states of a dynamical system with a novel action. At the self-consistent mean-field level, this approach yields normal diffusion and a finite longitudinal conductivity. While we have not been able to go beyond the saddle point approximation analytically, we show numerically that the critical localization exponent can be extracted from the energetically integrated correlation function yielding $\nu=2.33 \pm 0.05$ in excellent agreement with previous finite-size scaling studies.
Girvin Steven M.
Meden Volker
Sinova Jairo
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