Dynamical density and spin response functions of two-dimensional correlated fermion systems: Self-consistent second-order perturbation theory

Abstract

Dynamical density and spin responses of a two-dimensional fermion system are studied with the self-consistent second-order perturbation theory using a model Hamiltonian. Special attention is paid to the density response at a large wave vector, where it was reported that a sharp mode develops below the particle-hole continuum in two-dimensional liquid ${}^{3}$He. We find that at a large wave vector, a peak in the dynamical density structure factor shifts to lower energy as interaction sets in, but it is not sharp enough to represent a well-defined mode because of the strong damping effect of the quasiparticles. We point out that it is necessary to treat the large damping effect properly in explaining the propagating mode found in two-dimensional liquid ${}^{3}$He.