Abstract
Recent developments in the density-functional theory of electron correlations in many-body lattice models are reviewed. The theoretical framework of lattice density-functional theory (LDFT) is briefly recalled, giving emphasis to its universality and to the central role played by the single-particle density-matrix γ . The Hubbard model and the Anderson single-impurity model are considered as relevant explicit problems for the applications. Real-space and reciprocal-space approximations to the fundamental interaction-energy functional W [ γ ] are introduced, in the framework of which the most important ground-state properties are derived. The predictions of LDFT are contrasted with available exact analytical results and state-of-the-art numerical calculations. Thus, the goals and limitations of the method are discussed.
Highlights
Density-functional theory (DFT) is currently the most widespread method of determining the electronic properties of matter from first principles [1,2]
Based on the general formulation of the many-body problem in terms of the single-particle density matrix γ, we introduce the total energy functional E[γ] = T [γ] + W [γ], which can be naturally separated into the single-particle or kinetic-energy functional T [γ] and the interaction-energy functional W [γ]
The real-space density matrix γij, where i and j refer to the lattice sites, is considered as the central variable of the many-body problem and the scaling properties of W [γ] are exploited
Summary
Density-functional theory (DFT) is currently the most widespread method of determining the electronic properties of matter from first principles [1,2]. Despite the simplifications inherent to the model interactions and to the discretized basis set, the physics behind these problems remains highly nontrivial [52] Under these circumstances, and taking into account the remarkable success of DFT in dealing with the inhomogeneous electron gas in the continuum, it seems quite natural to attempt to adapt and transfer the concepts of DFT to the study of many-body lattice models. Taking into account the remarkable success of DFT in dealing with the inhomogeneous electron gas in the continuum, it seems quite natural to attempt to adapt and transfer the concepts of DFT to the study of many-body lattice models This would provide us with an alternative approach to the physics of strong correlations but should be useful for the development of DFT itself.
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