Phonons as collective modes: The case of a two-dimensional Wigner crystal in a strong magnetic field

Abstract
We present a fully-quantum-mechanical theory for the phonon modes of a two-dimensional Wigner crystal in the strong-magnetic-field limit. Our theory is based on a time-dependent Hartree-Fock approximation of the density-density response function χ, which is exact in the harmonic limit but allows for arbitrarily large anharmonicity. Our calulation is facilitated by identities, valid in the strong-magnetic-field limit, which allow χ to be expressed solely in terms of the ground-state electron density.