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We report the successful adaptation of the quasi-boson approximation, atechnique traditionally employed in nuclear physics, to the analysis of thetwo-dimensional electron gas. We show that the correlation energy estimatedfrom this approximation agrees closely with the results obtained from quantumMonte Carlo simulations. Our methodology comprehensively incorporates theexchange self-energy, direct scattering, and exchange scattering for aparticle-hole pair excited out of the mean-field groundstate within theequation-of-motion framework. The linearization of the equation of motion leadsto a generalized-random-phase-approximation (gRPA) eigenvalue equation whosespectrum indicates that the plasmon dispersion remains unaffected by exchangeeffects, while the particle-hole continuum experiences a marked upward shiftdue to the exchange self-energy. Notably, the plasmon mode retains itscollective nature within the particle-hole continuum, up to moderately shortwavelength ($q\sim 0.3 k_F$ at metallic density $r_s=4$). Using the gRPAexcitation spectrum, we calculate the zero-point energy of the quasi-bosonHamiltonian, thereby approximating the correlation energy of the originalHamiltonian. This research highlights the potential and effectiveness ofapplying the quasi-boson approximation to the gRPA spectrum, a fundamentaltechnique in nuclear physics, to extended condensed matter systems.

Quasi-boson approximation yields accurate correlation energy in the 2D electron gas