The collective excitations of the fractional-quantum-Hall liquid are studied within the Ginzburg-Landau theory. We show that (1) Gaussian fluctuations of the phase of the order parameter correspond to the cyclotron mode with an energy gap of ħ${\mathrm{\omega }}_{\mathit{c}}$ at q=0 and a contribution to the static structure factor proportional to ‖q${\mathrm{\Vert }}^2$ as q→0, in accordance with Kohn’s theorem, and (2) vortex-antivortex fluctuations give rise to the lowest-Landau-level collective mode with an energy gap that depends only on the Coulomb energy and a static structure factor that vanishes as ‖q${\mathrm{\Vert }}^4$ as q→0.

• Received 10 December 1990

DOI:https://doi.org/10.1103/PhysRevLett.66.1220