Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2007-05-11
Phys. Rev. A 76, 052517 (2007)
Physics
Condensed Matter
Strongly Correlated Electrons
Latex, 42 pages, 1 figure. Minor error in the proof of Prop. 2 corrected
Scientific paper
10.1103/PhysRevA.76.052517
The increasing interest in the Mueller density-matrix-functional theory has led us to a systematic mathematical investigation of its properties. This functional is similar to the Hartree-Fock functional, but with a modified exchange term in which the square of the density matrix \gamma(X, X') is replaced by the square of \gamma^{1/2}(X, X'). After an extensive introductory discussion of density-matrix-functional theory we show, among other things, that this functional is convex (unlike the HF functional) and that energy minimizing \gamma's have unique densities \rho(x), which is a physically desirable property often absent in HF theory. We show that minimizers exist if N \leq Z, and derive various properties of the minimal energy and the corresponding minimizers. We also give a precise statement about the equation for the orbitals of \gamma, which is more complex than for HF theory. We state some open mathematical questions about the theory together with conjectured solutions.
Frank Rupert L.
Lieb Elliott H.
Seiringer Robert
Siedentop Heinz
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