DENSITY-MATRIX FUNCTIONAL THEORY AND THE HIGH-DENSITY ELECTRON GAS

摘要

In addition to the 1-matrix γ with its characteristic short-range curvature in finite and extended systems and long-range oscillations in extended systems, the most important 2-body quantity is the cumulant 2-matrix χ. When contracted it yields the 1-matrix. It is size-extensively normalized, can be represented only by linked diagrams, and contains the cusp conditions. It yields the cumulant interaction energy V_c[χ], which is by definition a simple linear functional of χ. The curnulant expansion makes the interaction energy V_(int)[χ] = V_H[ρ] + V_F[γ] + V_c[χ] free of self interactions. The importance of this requirement for the conventional DFT, especially when applied to strongly correlated systems, has been stressed by J. P. Perdew at this conference. So, the hyper generalized gradient approximation provides a DFT functional, which corresponds to the cumulant expansion and is therefore free of self interactions. Calculational schemes for χ and its diagonalizing geminals and occupation numbers are highly desirable. The DMFT with a universal, but sophisticated and to date unknown 1-matrix functional V-c[γ] goes beyond the conventional DFT with the also universal, but only approximately known density functional (T + V_F + V_c)[ρ]. From a corresponding Euler equation, it yields not only the diagonal elements of the 1-matrix γ, but also its off-diagonal elements, from which the momentum distribution is obtained. A significant advantage of the DMFT is that it does not require a non-interacting reference system. Hence, it should apply both to weakly correlated as well as to strongly correlated systems. Within the CSE approach or from perturbation theory, particle-hole symmetric functionals χ[γ] may be derived, and when combined with V_c [χ], provide particle-hole symmetric DMFT functionals V_c[χ[γ]].