The Modular and Renormalisation Groups in the Quantum Hall Effect
高能物理 - 理论
2007-05-23 v1 介观与纳米尺度物理
摘要
An analytic form for the crossover of the conductivity tensor between two Hall plateaux, as a function of the external magnetic field, is proposed. The form of the crossover is obtained from the action of a symmetry group, a particular subgroup of the modular group, on the upper-half complex conductivity plane, by assuming that the beta-function describing the crossover is a holomorphic function of the conductivity. The group action also leads to a selection rule, |p_1q_2-p_2q_1|=1, for allowed transitions between Hall plateaux with filling factors p_1/q_1 and p_2/q_2, where q_1 and q_2 are odd.
引用
@article{arxiv.hep-th/9811218,
title = {The Modular and Renormalisation Groups in the Quantum Hall Effect},
author = {Brian P. Dolan},
journal= {arXiv preprint arXiv:hep-th/9811218},
year = {2007}
}
备注
Talk presented at the Workshop on the Exact Renormalisation Group, Faro, Portugal, 10-12th September, 1998. Typeset in Latex, 9 pages, 3 figures