Model Wave Functions for the Collective Modes and the Magnetoroton Theory of the Fractional Quantum Hall Effect

We construct model wave functions for the collective modes of fractional quantum Hall systems. The wave functions are expressed in terms of symmetric polynomials characterized by a root partition that defines a squeezed basis, and show excellent agreement with exact diagonalization results for finite systems. In the long wavelength limit, we prove that the model wave functions are identical to those predicted by the single-mode approximation, leading to intriguing interpretations of the collective modes from the perspective of the ground-state guiding-center metric.