Revealing quasi-excitations in the low-density homogeneous electron gas with model exchange-correlation kernels

Time-dependent density functional theory within the linear response regime provides a solid mathematical framework to capture excitations. The accuracy of the theory, however, largely depends on the approximations for the exchange-correlation (xc) kernels. Away from the long-wavelength (or q = 0 short wave-vector) and zero-frequency (omega = 0) limit, the correlation contribution to the kernel becomes more relevant and dominant over exchange. The dielectric function, in principle, can encompass xc effects relevant to describe low-density physics. Furthermore, besides collective plasmon excitations, the dielectric function can reveal collective electron-hole excitations, often dubbed "ghost excitons." Besides collective excitons, the physics of the low-density regime is rich, as exemplified by a static charge-density wave that was recently found for r(s) > 69, and was shown to be associated with softening of the plasmon mode. These excitations are seen to be present in much higher density 2D homogeneous electron gases of r(s) greater than or similar to 4. In this work, we perform a thorough analysis with xc model kernels for excitations of various nature. The uniform electron gas, as a useful model of real metallic systems, is used as a platform for our analysis. We highlight the relevance of exact constraints as we display and explain screening and excitations in the low-density region.