# A matrix model for νk1k2 = k1+k2/k1k2 fractional quantum hall states

Article

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(N 1) × 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 behavior of the plane. The formalism is illustrated for the state at ν = 2/5. © 2011 World Scientific Publishing Company.