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Revealing quasi-excitations in the low-density homogeneous electron gas with model exchange-correlation kernels
Aaron D. Kaplan, Adrienn Ruzsinszky
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Time-dependent density functional theory (TDDFT) 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 (ω=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.'' Beside collective excitons, the physics in the low-density regime is rich, as exemplified by a static charge-density wave that was recently found for rₛ > 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 HEGs, of rₛ ≥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 of our analysis. We highlight the relevance of exact constraints as we display and explain screening and excitations in the low-density region.
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