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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 theWigner-Seitz radius $ r_{\rm s} $ directly. We find that our correlation energycompletely reproduces the exact behavior at the high-density limit. For finitedensity, the result of FRG-DFT shows good agreement with the Monte Carlo (MC)results in the high-density region, although the discrepancy between FRG-DFTand MC results becomes larger as the system becomes more dilute. Our study isthe first example in which the FRG-DFT is applied to more-than-one-dimensionalmodels, and shows that the FRG-DFT is a feasible and promising method even forthe analysis of realistic models for quantum many-body systems.

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