Multi-pair and exchange effects in the dynamic structure of two-dimensional ³He

We examine the effect of fermionic exchange interactions on the dynamic structure function of two-dimensional ³He within a manifestly microscopic theory of excitations. These exchanges have, at different wave lengths and densities, different consequences: At low densities, exchanges are decisive to determine whether the phonon is Landau-damped or not. In the intermediate wave number regime, exchanges are relatively unimportant but they become important again at short wave length corresponding to about four times the Fermi wave number. A very important further aspect is the inclusion of pair fluctuations. These are fluctuations of the wave function that can not be described by the quantum numbers of a single particle. They do not change the features of long wave length excitations, but induce a finite width to the collective mode outside the particle-hole continuum. In the intermediate momentum regime, where one would expect a "roton minimum" in a Bose fluid with the same interaction and density, pair fluctuations cause a visible shift of the strength of the dynamic structure function towards lower energies and cause a very sharp collective mode. The effect, which was reported by Godfrin et al. (Nature 483:576, 2012), is slightly enhanced by exchange corrections.