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

Abstract

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 rs 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 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-onedimensional 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.

Construction of energy density functional for arbitrary spin polarization using functional renormalization group

“…The interaction term S int contains not only the electronelectron interaction term but also the electron-ion and ion-ion ones, which cancel each other, and consequently avoid the divergence from Hartree term in the infinite system [22]. Additionally, X = (τ + , x) with a positive infinitesimal has been introduced so that the corresponding Hamiltonian is normal ordered.…”

“…The evolution of Γ λ [ρ ↑ , ρ ↓ ] can be described by a functional differential equation. This equation is derived in the same manner as EDF for total density [10,15,18,19,22] and reads…”

“…As in our previous works [22,23], we ignore the λ dependence of C λ, s1s2 (P 1 ) as C λ, s1s2 (P 1 ) ≈ C λ=0, s1s2 (P 1 ). Applying this approximation and summing up the spin indices, Eqs.…”

“…For such a closed form of equation, some systematic approximation methods were proposed [9,[15][16][17]. The FRG-DFT has been numerically applied to lowdimensional toy models [15][16][17][18][19][20][21] including a mimic of the nuclear systems [18][19][20], and, recently, applied to electronic systems [22,23], where we achieved the first application to the two and three dimensional cases in the study of the homogeneous electron gas (HEG) and EDFs for electrons are constructed in the local density approximation.…”

“…In the previous works of the FRG-DFT [9,10,[15][16][17][18][19][20][21][22][23], the EDF of total particle-number density has been studied. The Hohenberg-Kohn theorem guarantees that the ground-state properties are determined by the total particle-number density.…”