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arXiv:cond-mat/0503270 · Physical Review Letters

Electronic Structure of Strongly Correlated Systems Emerging from Combining Path-Integral Renormalization Group with the Density-Functional Approach

Yoshiki Imai, Igor V. Solovyev, Masatoshi Imada

Published Oct 19, 2005• 72 citations
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Abstract

A new scheme of first-principles computation for strongly correlated electron systems is proposed. This scheme starts from the local-density approximation (LDA) at high-energy band structure, while the low-energy effective Hamiltonian is constructed by a downfolding procedure using combinations of the constrained-LDA and the GW method. The obtained low-energy Hamiltonian is solved by the path-integral renormalization-group method, where spatial and dynamical fluctuations are fully considered. An application to Sr2VO4 shows that the scheme is powerful in agreement with experimental results. It further predicts a nontrivial orbital-stripe order.

DOI
10.1103/physrevlett.95.176405

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International Journal of Quantum Chemistry•Jan 1, 2005•2 citations
A new scheme of first-principles computation for strongly correlated electron systems is proposed. This scheme starts from the local-density approximation (LDA) at high-energy band structure, while the low-energy effective Hamiltonian is constructed by a downfolding procedure using combinations of the constrained-LDA and the GW method. The obtained low-energy Hamiltonian is solved by the path-integral renormalization-group method, where spatial and dynamical fluctuations are fully considered. An application to Sr2VO4 shows that the scheme is powerful in agreement with experimental results. It further predicts a nontrivial orbital-stripe order.
We propose a dynamical mean-field approach for calculating the electronic structure of strongly correlated materials from first principles. The scheme combines the GW method with dynamical mean-field theory, which enables one to treat strong interaction effects. It avoids the conceptual problems inherent to conventional "LDA+DMFT," such as Hubbard interaction parameters and double-counting terms. We apply a simplified version of the approach to the electronic structure of nickel and find encouraging results.
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Recent trends of ab initio studies and progress in methodologies for electronic structure calculations of strongly correlated electron systems are discussed. The interest for developing efficient methods is motivated by recent discoveries and characterizations of strongly correlated electron materials and by requirements for understanding mechanisms of intriguing phenomena beyond a single-particle picture. A three-stage scheme is developed as renormalized multi-scale solvers (RMS) utilizing the hierarchical electronic structure in the energy space. It provides us with an ab initio downfolding of the global band structure into low-energy effective models followed by low-energy solvers for the models. The RMS method is illustrated with examples of several materials. In particular, we overview cases such as dynamics of semiconductors, transition metals and its compounds including iron-based superconductors and perovskite oxides, as well as organic conductors of kappa-ET type.
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