A Matrix Model for ν_{k_1k_2}=\frac{k_1+k_2}{k_1 k_2} Fractional Quantum Hall States

Details A Matrix Model for ν_{k_1k_2}=\frac{k_1+k_2}{k_1 k_2} Fractional Quantum Hall States A Matrix Model for ν_{k_1k_2}=\frac{k_1+k_2}{k_1 k_2} Fractional Quantum Hall States

2002-04-29

arxiv.org/abs/hep-th/0204248v2

Int.J.Geom.Meth.Mod.Phys.08:557-586,2011

Physics

High Energy Physics

High Energy Physics - Theory

40 pages, 1 figure, clarifications and references added

Scientific paper

10.1142/S0219887811005270

We propose a matrix model to describe a class of fractional quantum Hall (FQH) states for a system of (N_1+N_2) 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 \nu_{k_1k_2}=\frac{k_1+k_2}{k_1k_2} (k_1 and k_2 odd integers), has a U(N_1)\times U(N_2) 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 \nu_{p_1p_2}=\frac{p_2}{p_1p_2-1}, p_1 and p_2 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 \nu={2/5}.

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