Dresden 2003 – wissenschaftliches Programm
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TT: Tiefe Temperaturen
TT 7: Niedrigdimensionale Systeme
TT 7.3: Vortrag
Dienstag, 25. März 2003, 10:15–10:30, HSZ03
A Matrix Model for Fractional Quantum Hall States — •Ahmed Jellal1, El Hassan Saidi2, B. Hendrik Geyer3, and A. Rudolf Römer4 — 1Institut für Physik Technische Universität, D-09107 Chemnitz, Germany — 2Lab/UFR, High Energy Physics, Physics Department, Mohammed V University, Av. Ibn Battouta, P.O. Box. 1014 Rabat, Morocco — 3Institute for Theoretical Physics, University of Stellenbosch, Private Bag X1, Matieland 7602, South Africa — 4Department of Physics, University of Warwick, Coventry CV4 7AL, UK
We propose a matrix model to describe a class of fractional quantum Hall (FQH) states for a system of (N1+N2) electrons with filling factor more general than in the Laughlin case. Our model, which is developed for FQH states with filling factor of the form νk1k2=k1+k2/k1k2 (k1 and k2 odd integers), has a U(N1)× U(N2) gauge invariance, assumes that FQH fluids are composed of coupled branches of the Laughlin type, and uses ideas borrowed from hierarchy scenarios. Interactions are carried, amongst others, by fields in the bi-fundamentals of the gauge group. They simultaneously play the role of a regulator, exactly as does the Polychronakos field. We build the vacuum configurations for FQH states with filling factors given by the series νp1p2=p2/p1p2−1, p1 and p2 integers. Electrons are interpreted as a condensate of fractional D0-branes and the usual degeneracy of the fundamental state is shown to be lifted by the non-commutative geometry behaviour of the plane. The formalism is illustrated for the state at ν=2/5.