Homogeneous Electron Liquid in Arbitrary Dimensions: Exchange and Correlation Using the Singwi-Tosi-Land-Sjölander Approach

Abstract

The ground states of the homogeneous electron gas and the homogeneous electron liquid are cornerstones in quantum physics and chemistry. They are archetypal systems in the regime of slowly varying densities in which the exchange-correlation energy can be estimated with a myriad of methods. For high densities, the behavior of the energy is well-known for 1, 2, and 3 dimensions. Here, we extend this model to arbitrary integer dimensions, and compute its correlation energy beyond the random phase approximation (RPA), using the celebrated approach developed by Singwi, Tosi, Land, and Sjölander (STLS), which is known to be remarkably accurate in the description of the full electronic density response for $2D$ and $3D$, both in the paramagnetic and ferromagnetic ground states. For higher dimensions, we compare the results obtained for the correlation energy using the STLS method with the values previously obtained using RPA. We found that at high dimensions STLS tends to be more physical in the sense that the infamous sum rules are better satisfied by the theory. We furthermore illustrate the importance of the plasmon contribution to STLS theory.

arXiv comment14 pages, 9 figures

References in corpus (43)

• One-Dimensional Fermi liquids
• Synthetic gauge fields in synthetic dimensions
• Random-phase approximation and its applications in computational chemistry and materials science
• Moiré heterostructures as a condensed matter quantum simulator
• A Four Dimensional Generalization of the Quantum Hall Effect
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Quantum simulation of an extra dimension
• The Uniform Electron Gas at Warm Dense Matter Conditions
• Design and characterization of electronic fractals
• Ab initio simulation of warm dense matter
• Experimental band structure spectroscopy along a synthetic dimension
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• A Full Configuration Interaction Perspective on the Homogeneous Electron Gas
• Machine Learning the Physical Non-Local Exchange-Correlation Functional of Density-Functional Theory
• Realizing Su-Schrieffer-Heeger topological edge states in Rydberg-atom synthetic dimensions
• Transport and optical properties of an electron gas in a Sierpinski carpet
• Quantum Monte Carlo study of the three-dimensional spin-polarized homogeneous electron gas
• Momentum Distribution and Renormalization Factor in Sodium and the Electron Gas
• Theory of spin and charge fluctuations in the Hubbard model
• Topological states on fractal lattices
• Reference electronic structure calculations in one dimension
• Topology in the Sierpiński-Hofstadter problem
• Flat bands in fractal-like geometry
• Momentum distribution of the uniform electron gas: improved parametrization and exact limits of the cumulant expansion
• Uniform electron gas at finite temperatures
• The existence of robust edge currents in Sierpinsky Fractals
• High-Level Correlated Approach to the Jellium Surface Energy, Without Uniform-Electron-Gas Input
• The momentum distribution of the homogeneous electron gas
• Towards a formal definition of static and dynamic electronic correlations
• Coulomb and Riesz gases: The known and the unknown
• Correlation energies of inhomogeneous many-electron systems
• One-dimensional Bose gas in optical lattices of arbitrary strength
• Exact bosonization in arbitrary dimensions
• The Hartree-Fock ground state of the three-dimensional electron gas
• Statistical Mechanics of the Uniform Electron Gas
• Machine learning the derivative discontinuity of density-functional theory
• Phases of Attractive Fermi Gases in Synthetic Dimensions
• Improved Equation of State for Finite-Temperature Spin-Polarized Electron Liquids on the Basis of Singwi-Tosi-Land-Sjolander Approximation
• Synthetic dimension-induced conical intersections in Rydberg molecules
• Lower Bound on the Hartree-Fock Energy of the Electron Gas
• Two-Particle Self-Consistent method for the multi-orbital Hubbard model
• Quantum Singwi-Tosi-Land-Sjoelander approach for interacting inhomogeneous systems under electromagnetic fields: Comparison with exact results
• Homogeneous electron gas in arbitrary dimensions