Strictly correlated uniform electron droplets

Abstract

We study the energetic properties of finite but internally homogeneous D-dimensional electron droplets in the strict-correlation limit. The indirect Coulomb interaction is found to increase as a function of the electron number, approaching the tighter forms of the Lieb-Oxford bound recently proposed by Rasanen et al. [Phys. Rev. Lett. 102, 206406 (2009)]. The bound is satisfied in three-, two-, and one-dimensional droplets, and in the latter case it is reached exactly - regardless of the type of interaction considered. Our results provide useful reference data for delocalized strongly correlated systems, and they can be used in the development and testing of exchange-correlation density functionals in the framework of density-functional theory.

References in corpus (9)

• Density functional theory for strongly interacting electrons
• The Ground States of Large Quantum Dots in Magnetic Fields
• Density functional theory for strongly-interacting electrons: Perspectives for Physics and Chemistry
• Ground-state energy of the electron liquid in ultrathin wires
• How tight is the Lieb-Oxford bound?
• Lower Bounds on the Exchange-Correlation Energy in Reduced Dimensions
• Non-empirical hyper-generalized-gradient functionals constructed from the Lieb-Oxford bound
• Intracule densities in the strong-interaction limit of density functional theory
• Empirical analysis of the Lieb-Oxford bound in ions and molecules

Cited by in corpus (17)

• Optimal-transport formulation of electronic density-functional theory
• Strong correlation in Kohn-Sham density functional theory
• Kohn-Sham density functional theory for quantum wires in arbitrary correlation regimes
• Improved Lieb-Oxford exchange-correlation inequality with gradient correction
• Statistical Mechanics of the Uniform Electron Gas
• Exchange-correlation functionals from the strongly-interacting limit of DFT: Applications to model chemical systems
• N-density representability and the optimal transport limit of the Hohenberg-Kohn functional
• Challenging the Lieb-Oxford Bound in a systematic way
• Augmented potential, energy densities, and virial relations in the weak- and strong-interaction limits of DFT
• Density functional theory for strongly-correlated bosonic and fermionic ultracold dipolar and ionic gases
• Improved Lieb-Oxford bound on the indirect and exchange energies
• On the violation of a local form of the Lieb-Oxford bound
• Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model
• A New Estimate on the Two-Dimensional Indirect Coulomb Energy
• Large two-dimensional electronic systems: Self-consistent energies and densities at low cost
• Indirect Coulomb Energy for Two-Dimensional Atoms
• One-Dimensional Lieb-Oxford Bounds