A MATRIX MODEL FOR νk1k2 = k1+k2/k1k2 FRACTIONAL QUANTUM HALL STATES

摘要

We propose a matrix model to describe a class of Fractional Quantum Hall (FQH),nstates for a system of (N1 + N2) electrons with filling factor more general than innthe Laughlin case. Our model, which is developed for FQH states with filling factornof the form νk1k2 = k1+k2nk1k2n(k1 and k2 odd integers), has a U(N1) × U(N2) gaugeninvariance. Assumes that FQH fluids are composed of coupled branches of the Laughlinntype, and uses ideas borrowed from hierarchy scenarios. Interactions are carried, amongstnothers, by fields in the bi-fundamentals of the gauge group. They simultaneously playnthe role of a regulator, exactly as does the Polychronakos field. We build the vacuumnconfigurations for FQH states with filling factors given by the series νp1p2 = p2np1p2−1 ,np1 and p2 integers. Electrons are interpreted as a condensate of fractional D0-branesnand the usual degeneracy of the fundamental state is shown to be lifted by the noncommutativengeometry behavior of the plane. The formalism is illustrated for the statenat ν = 2n5 .