Physical Review A · 1993 · 146 citations · 12 references
Natural SciencesPhysicsCondensed Matter PhysicsQuantum MechanicsRepresentation TheoryApproximation MethodsDensity Matrix FormalismElectron CorrelationStrongly Correlated Electron SystemsCanonical Commutation RelationsDensity MatricesDensity Matrix FormulationReduced Density MatricesReduced Density MatrixReduced Density Matrix TheorySymmetric Group Representations
The commutation-anticommutation relations of q-electron operators imply a set of N representability conditions [A. J. Coleman, Rev. Mod. Phys. 31, 668 (1963)] for the corresponding q-order reduced density matrices (q-RDM) [C. Valdemoro, An. Fis. 79, 95 (1983); in Structure, Interaction and Reactivity, edited by S. Fraga (Elsevier, Amsterdam, 1992)]. From these conditions, a general and closed-form relation is obtained here. In this equation the part involving RDM's has the same structure as that involving hole reduced density matrices. This relation is the basis of a method for approximating a q-RDM in terms of the r-RDM's [C. Valdemoro, Phys. Rev. A 45, 4462 (1992)] with rq. The derivation of this relation can be simplified significantly by employing a graph method which is described here. These graphs are in a one-to-one correspondence with the elements of the symmetric group of permutations.
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