Collective excitations in a two-dimensional dipole system

We address the question of collective excitations in two-dimensional (2D) dipolar systems. The main issue is that such systems have no Hartree and no random-phase-approximation (RPA) limits and calculations have to include particle correlations from the outset. We focus on the longitudinal collective mode representing the density oscillations of the dipoles and on the transverse collective mode representing shear waves. Our theoretical approach is based on the quasi-localized charge approximation (QLCA) adapted to point-dipole systems interacting through a 1/r3 potential. Our analytical calculation is accompanied by classical molecular dynamics (MD) simulation. At long wavelengths, the longitudinal and transverse collective excitations exhibit acoustic behaviors with phase velocities that vary linearly with the dipole strength and are wholly maintained by particle correlations. At finite wavenumbers, the mode dispersion resulting from our classical MD simulations shows a roton-like behavior. Comparison with the quantum Monte Carlo dispersion generated through the Feynman relation (Astrakharchik et al 2007 Phys. Rev. Lett. 98 060405) shows a remarkably good quantitative agreement between the two