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MRS Proceedings

Renormalization from Density Functional Theory to Strong Coupling Models for the Electronic Structure of La2CuO4

Mark S. Hybertsen, Michael Schlüter, Ellen B. Stechel, Dwight R. Jennison

Published Jan 1, 1989• 2 citations
Publisher
DOI
10.1557/proc-169-19

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Strong-coupling models for the electronic structure of La2{\mathrm{La}}_{2}La2​CuO4{\mathrm{CuO}}_{4}CuO4​ are derived from the local-density-functional results in two successive stages of renormalization. First, a three-band Hubbard model is derived with parameters explicitly calculated from first principles using a constrained density-functional approach and a mean-field fit to the Cu-O pd\ensuremath{\sigma} bands. Second, exact diagonalization studies of finite clusters within the three-band Hubbard model are used to select and map the low-energy spectra onto effective one-band Hamiltonians, e.g., the Heisenberg, one-band Hubbard, or ``t-t'-J'' model. At each stage, calculated observables are in quantitative agreement with experiment.
Occupation numbers of natural orbitals capture the physics of strong electron correlations in momentum space. A natural orbital density functional theory based on the antisymmetrized geminal product provides these occupation numbers and the corresponding electron momentum density. A practical implementation of this theory approximates the natural orbitals by the Kohn–Sham orbitals and uses a mean-field approach to estimate pairing amplitudes leading to corrections for the independent particle model. The method is applied to weakly doped La2CuO4.
Abstract The diagrammatic strong‐coupling perturbation theory (SCPT) for correlated electron systems is developed for intersite Coulomb interaction and for a nonorthogonal basis set. The construction is based on iterations of exact closed equations for many‐electron Green functions (GFs) for Hubbard operators in terms of functional derivatives with respect to external sources. The graphs, which do not contain the contributions from the fluctuations of the local population numbers of the ion states, play a special role: a one‐to‐one correspondence is found between the subset of such graphs for the many‐electron GFs and the complete set of Feynman graphs of weak‐coupling perturbation theory (WCPT) for single‐electron GFs. This fact is used for formulation of the approximation of renormalized Fermions (ARF) in which the many‐electron quasi‐particles behave analogously to normal Fermions. Then, by analyzing: (a) Sham's equation, which connects the self‐energy and the exchange–correlation potential in density functional theory (DFT); and (b) the Galitskii and Migdal expressions for the total energy, written within WCPT and within ARF SCPT, a way we suggest a method to improve the description of the systems with correlated electrons within the local density approximation (LDA) to DFT. The formulation, in terms of renormalized Fermions LDA (RF LDA), is obtained by introducing the spectral weights of the many‐electron GFs into the definitions of the charge density, the overlap matrices, effective mixing and hopping matrix elements, into existing electronic structure codes, whereas the weights themselves have to be found from an additional set of equations. Compared with LDA+U and self‐interaction correction (SIC) methods, RF LDA has the advantage of taking into account the transfer of spectral weights, and, when formulated in terms of GFs, also allows for consideration of excitations and nonzero temperature. Going beyond the ARF SCPT, as well as RF LDA, and taking into account the fluctuations of ion population numbers would require writing completely new codes for ab initio calculations. The application of RF LDA for ab initio band structure calculations for rare earth metals is presented in part II of this study (this issue). © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2005