Real-space renormalization at the quantum Hall transition
摘要
We review recent applications of the real-space renormalization group (RG) approach to the integer quantum Hall (QH) transition. The RG approach, applied to the Chalker-Coddington network model, reproduces the critical distribution of the power transmission coefficients, i.e., two-terminal conductances, P_c(G), with very high accuracy. The RG flow of P(G) at energies away from the transition yields a value of the critical exponent, nu_G=2.39 +/- 0.01, that agrees with most accurate large-size lattice simulations. Analyzing the evolution of the distribution of phases of the transmission coefficients upon a step of the RG transformation, we obtain information about the energy-level statistics (ELS). From the fixed point of the RG transformation we extract a critical ELS. Away from the transition the ELS crosses over towards a Poisson distribution. Studying the scaling behavior of the ELS around the QH transition, we extract the critical exponent nu_ELS=2.37 +/- 0.02.
引用
@article{arxiv.cond-mat/0304612,
title = {Real-space renormalization at the quantum Hall transition},
author = {Rudolf A. Roemer and Philipp Cain},
journal= {arXiv preprint arXiv:cond-mat/0304612},
year = {2015}
}
备注
to be published in Advances of Solid State Physics, Springer, Berlin (2003)