Interaction and dynamical binding of spin waves or excitons in quantum Hall systems

Abstract

Interaction between spin waves (or excitons) moving in the lowest Landau level is studied using numerical diagonalization. Because of complicated statistics obeyed by these composite particles, their effective interaction is completely different from the dipole–dipole interaction predicted in the model of independent (bosonic) waves. In particular, spin waves moving in the same direction attract one another, which leads to their dynamical binding. Effective interaction pseudopotentials V↑↑(k) and V↑↓(k) for two spin waves with equal wave vectors k and moving in the same or opposite directions are calculated and shown to obey power laws V(k) ∝ kα at small k. A high value of α↑↑ ≈ 4 explains the occurrence of linear bands in spin excitation spectra of quantum Hall droplets. PACS Nos.: 71.10.Pm, 71.35.–y, 75.30.Ds