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Time-dependent density functional theory (TDDFT) within the linear responseregime provides a solid mathematical framework to capture excitations. Theaccuracy of the theory, however, largely depends on the approximations for theexchange-correlation (xc) kernels. Away from the long-wavelength (or $q=0$short wave-vector) and zero-frequency ($\omega=0$) limit, the correlationcontribution to the kernel becomes more relevant and dominant over exchange.The dielectric function in principle can encompass xc effects relevant todescribe low-density physics. Furthermore, besides collective plasmonexcitations, the dielectric function can reveal collective electron-holeexcitations, often dubbed ``ghost excitons.'' Beside collective excitons, thephysics in the low-density regime is rich, as exemplified by a staticcharge-density wave that was recently found for $r_\mathrm{s} > 69$, and wasshown to be associated with softening of the plasmon mode. These excitationsare seen to be present in much higher density 2D HEGs, of $r_\mathrm{s} \geq4$. In this work we perform a thorough analysis with xc model kernels forexcitations of various nature. The uniform electron gas as a useful model ofreal metallic systems is used as a platform of our analysis. We highlight therelevance of exact constraints as we display and explain screening andexcitations in the low-density region.

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