Generalized yrast states of a Bose condensate in harmonic trap for a universality class of repulsive interactions

For a system of N bosons in a 2d harmonic trap with frequency omega, interacting via repulsive forces V<<omega, we develop supersymmetric method to find the lowest energy states of rotating Bose condensate as function of two quantum numbers, the total angular momentum and the angular momentum of internal excitations (generalized yrast states). The energies of these condensed vortex states are expressed through the single two-body matrix element of interaction V. A broad universality class of the repulsive interactions for which these results hold is described by a simple integral condition on V. It includes Gaussian, delta-function and log-Coulomb forces.