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Springer series in solid-state sciences

On the Application of Projection Techniques to the Electron Correlation Problem

K. W. Becker, Peter Fulde

Published Jan 1, 1989• 1 citation
Publisher
DOI
10.1007/978-3-642-83836-1_12

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By applying projection techniques a unified description of weakly and strongly correlated electronic systems can be given. For that purpose the theory is formulated in Liouville instead of Hilbert space. By introducing an appropriate metric in terms of cumulants it is ensured that all energies are size consistent. An energy expression is derived which is a generalization of Goldstone’s linked cluster theorem for arbitrary Hamiltonians. It is suitable for applying the projection method of Zwanzig and Mori. The equations for the correlation energy within the Local Ansatz and within coupled electron pair approximation CEPA-2 follow straightforwardly from the present theory.
We generalized the Gutzwiller projectional variational method for the ground state of strongly correlated electron systems to the case of finite temperature. Under the Gutzwiller approximation, we show that this maps to a finite temperature renormalized mean-field theory. As one of the key ingredients in the theory, we obtained an explicit expression of the projection entropy or the entropy change due to the projection. We illustrate the application of the theory to the Anderson impurity problem and the half-filled Hubbard model and compare the theory to more elaborate techniques. We find qualitative agreement. The theory can be applied to a wide variety of Hubbard, $t\text{\ensuremath{-}}J$, and Anderson impurity models.