Systematic corrections to the Thomas-Fermi approximation without a gradient expansion

Abstract

We improve on the Thomas-Fermi approximation for the single-particle density of fermions by introducing inhomogeneity corrections. Rather than invoking a gradient expansion, we relate the density to the unitary evolution operator for the given effective potential energy and approximate this operator by a Suzuki-Trotter factorization. This yields a hierarchy of approximations, one for each approximate factorization. For the purpose of a first benchmarking, we examine the approximate densities for a few cases with known exact densities and observe a very satisfactory, and encouraging, performance. As a bonus, we also obtain a simple fourth-order leapfrog algorithm for the symplectic integration of classical equations of motion.

arXiv comment20 pages; added 1 figure, 3 appendices, and references; old figures updated

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Cited by in corpus (4)

• First-principles quantum corrections for carrier correlations in double-layer two-dimensional heterostructures
• Single-particle-exact density functional theory
• Phase Transitions of Repulsive Two-Component Fermi Gases in Two Dimensions
• Airy gas model: From three to reduced dimensions