Uq[sl(2)] Quantum Algebra in Quantum Hall Effect

Holger Frahm, Fabian H. L. Eßler, Hubert Saleur

Ying-Hai Wu, Bo Yang, Zlatko Papić

Bo Yang, Ying-Hai Wu, Zlatko Papić

Omer Faruk Dayi

Quantum Hall effect wavefunctions corresponding to the filling factors 1/2p+1, 2/2p+1,..., 2p/2p+1, 1, are shown to form a basis of irreducible cyclic representation of the quantum algebra U_q(sl(2)) at q^{2p+1}=1. Thus, the wavefunctions Ψ_{P/Q} possessing filling factors P/Q<1 where Q is odd and P, Q are relatively prime integers are classified in terms of U_q(sl(2)). Adopted as dynamical symmetry this leads to non--existence of a ``universal microscopic theory" of the quantum Hall effect, defined as the eigenvalue problem of a differential operator O: O Ψ_ν=\ell_νΨ_ν. for ν=1,1/3,2/3,..., in the complex plane.

Omer Faruk Dayi

Quantum Hall effect wave functions corresponding to the filling factors 1/2p+1, 2/2p+1, ..., 2p/2p+1, 1, where p is a positive integer are shown to form a basis of irreducible cyclic representation of the quantum group U_q(sl(2)) at q^{2p+1}=1. Thus, the wave functions possessing filling factors P/Q<1 where Q is odd and P, Q are relatively prime integers are classified in terms of U_q(sl(2)).