Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect

Details Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect Numerical study of the localization length critical index in a network model of plateau-plateau transitions in the quantum Hall effect

2009-12-22

arxiv.org/abs/0912.4403v1

Phys. Rev. Lett. 107, 066402 (2011)

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.107.066402

We calculate numerically the localization length critical index within the Chalker-Coddington (CC) model for plateau-plateau transitions in the quantum Hall effect. Lyapunov exponents have been calculated with relative errors on the order $10^{-3}$. Such high precision was obtained by considering the distribution of Lyapunov exponents for large ensembles of relatively short chains and calculating the ensemble average values. We analyze thoroughly finite size effects and find the localization length critical index $\nu= 2.517\pm 0.018$.

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