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.

14 pages, 9 figures

References in corpus (12)

• Moiré heterostructures as a condensed matter quantum simulator
• Exploring 4D Quantum Hall Physics with a 2D Topological Charge Pump
• Experimental band structure spectroscopy along a synthetic dimension
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• High-Level Correlated Approach to the Jellium Surface Energy, Without Uniform-Electron-Gas Input
• Towards a formal definition of static and dynamic electronic correlations
• Coulomb and Riesz gases: The known and the unknown
• The Hartree-Fock ground state of the three-dimensional electron gas
• Machine learning the derivative discontinuity of density-functional theory
• Synthetic dimension-induced conical intersections in Rydberg molecules
• Quantum Singwi-Tosi-Land-Sjoelander approach for interacting inhomogeneous systems under electromagnetic fields: Comparison with exact results
• Homogeneous electron gas in arbitrary dimensions