$\Gamma$(2) modular symmetry, renormalization, group flow and the quantum hall effect - IN2P3 - Institut national de physique nucléaire et de physique des particules Access content directly
Journal Articles Journal of Physics A: Mathematical and Theoretical Year : 2000

$\Gamma$(2) modular symmetry, renormalization, group flow and the quantum hall effect

T. Masson
J C. Wallet
  • Function : Author

Abstract

We construct a family of holomorphic $\beta$-functions whose RG flow preserves the $\Gamma(2)$ modular symmetry and reproduces the observed stability of the Hall plateaus. The semi-circle law relating the longitudinal and Hall conductivities that has been observed experimentally is obtained from the integration of the RG equations for any permitted transition which can be identified from the selection rules encoded in the flow diagram. The generic scale dependance of the conductivities is found to agree qualitatively with the present experimental data. The existence of a crossing point occuring in the crossover of the permitted transitions is discussed.

Dates and versions

in2p3-00003885 , version 1 (25-01-2000)

Identifiers

Cite

Y. Georgelin, T. Masson, J C. Wallet. $\Gamma$(2) modular symmetry, renormalization, group flow and the quantum hall effect. Journal of Physics A: Mathematical and Theoretical, 2000, 33, pp.39-55. ⟨in2p3-00003885⟩
7 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More