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#### Cumulant 2-matrix of the high-density electron gas and the density matrix functional theory

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##### Citation

Ziesche, P. (2002). Cumulant 2-matrix of the high-density electron gas and the density
matrix functional theory.* INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY,* *90*(1),
342-354. doi:10.1002/qua.969.

Cite as: http://hdl.handle.net/11858/00-001M-0000-002C-5B1D-D

##### Abstract

The cumulant 2-matrix chi is that part of the two-body reduced density matrix gamma2, which cannot be reduced to products of the one-body reduced density matrix (1-matrix) gamma. This irreducible part chi is calculated perturbatively for the high-density electron gas (EG) in its ground state, such that the pair densities and the interaction energy are correctly reproduced in their high-density limits, which are exactly known and summarized here. From the thus available cumulant 2-matrix the pair density in momentum space can be derived and used for a fluctuation analysis and compared with the analog analysis in position space, where it is concluded that "correlation suppresses fluctuations". The perturbatively available cumulant 2-matrix chi can be used also for the high-density electron gas to start the iterative solution of the Yasuda integral equation of density matrix functional theory (DMFT), which is a nonlinear functional relation between the cumulant 2-matrix chi and the 1-matrix gamma recently derived from the contracted Schrodinger equation approach: chi(gamma)[gamma]. From the perturbatively determined chi one can find another functional chi[gamma] as an alternative approximation for a DMFT. (C) 2002 Wiley Periodicals, Inc.