Momentum distribution function of a narrow hall bar in the FQHE regime

The momentum distribution function (n(k)) of a narrow Hall bar in the fractional quantum Hall effect regime is investigated using Luttinger liquid and microscopic many-particle wavefunction approaches. For wide Hall bars with filling factor v = 1/M, where M is an odd integer, n(k) has singularities at ±Mk_F. We find that for narrow Hall bars additional singularities occur at smaller odd integral multiples of k_F: n(k) ∼ A_p|k±pk_F|^2Δp-1 near k = ±Pk_F, where p is an odd integer M, M - 2, M 4, ..., 1. If inter-edge interactions can be neglected, the exponent 2Δ_P = (1/v+p²v)/2 is independent of the width (w) of the Hall bar but the amplitude of the singularity A_p vanishes exponentially with w for p ≠ M.