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

Abstract

We report the successful adaptation of the quasi-boson approximation, a technique traditionally employed in nuclear physics, to the analysis of the two-dimensional electron gas. We show that the correlation energy estimated from this approximation agrees closely with the results obtained from quantum Monte Carlo simulations. Our methodology comprehensively incorporates the exchange self-energy, direct scattering, and exchange scattering for a particle-hole pair excited out of the mean-field groundstate within the equation-of-motion framework. The linearization of the equation of motion leads to a generalized-random-phase-approximation (gRPA) eigenvalue equation whose spectrum indicates that the plasmon dispersion remains unaffected by exchange effects, while the particle-hole continuum experiences a marked upward shift due to the exchange self-energy. Notably, the plasmon mode retains its collective nature within the particle-hole continuum, up to moderately short wavelength ($q\sim 0.3k_F$ at metallic density $r_s=4$). Using the gRPA excitation spectrum, we calculate the zero-point energy of the quasi-boson Hamiltonian, thereby approximating the correlation energy of the original Hamiltonian. This research highlights the potential and effectiveness of applying the quasi-boson approximation to the gRPA spectrum, a fundamental technique in nuclear physics, to extended condensed matter systems.

arXiv comment7 pages, 4 figures

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Cited by in corpus (4)

• Competition of Exchange and Correlation Energies in Two-Dimensional $N$-component Electron Gas Ferromagnetism
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene
• Orbital Magnetization and Streda Formula of Interacting Electrons in the Mean-field Approximation
• Elastic Response and Instabilities of Anomalous Hall Crystals