Functional-renormalization-group aided density functional analysis for the correlation energy of the two-dimensional homogeneous electron gas

The functional-renormalization-group aided density functional theory (FRG-DFT) is applied to the two-dimensional homogeneous electron gas (2DHEG). The correlation energy of the 2DHEG is derived as a function of the Wigner-Seitz radius $r_{\mathrm{s}}$ directly. We find that our correlation energy completely reproduces the exact behavior at the high-density limit. For finite density, the result of FRG-DFT shows good agreement with the Monte Carlo (MC) results in the high-density region, although the discrepancy between the FRG-DFT and MC results becomes larger as the system becomes more dilute. Our study is the first example in which the FRG-DFT is applied to more-than-one-dimensional models, and shows that the FRG-DFT is a feasible and promising method even for the analysis of realistic models for quantum many-body systems.

Figure 1

Correlation energy $E_{\mathrm{corr}}/N$ of the 2DHEG derived by the FRG-DFT method (solid red line) shown as the function of the Wigner-Seitz radius $r_{\mathrm{s}}$. For comparison, the results derived by the Gell-Mann-Brueckner resummation (black dashed line) and the Monte Carlo calculations are also shown. The green inverted triangles and blue triangles are the energies derived by the extrapolations of the results of the DMC calculations to the infinite systems given by Kwon et al. [33] and Drummond et al. [48], respectively.