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Journal of the Physical Society of Japan

Local-Orbital Based Correlatedab initioBand Structure Calculations in Insulating Solids

Martin Albrecht, Jun-ichi Igarashi

Published Apr 15, 2001• 16 citations
Publisher

Abstract

A local-orbital based ab initio approach to calculate correlation effects on quasi particle energies in insulating solids is presented. The use of localized Wannier-type Hartree Fock orbitals allows to efficiently devide correlation effects into classes of strong, medium or small weight. Subsequently the strongly contributing correlations are obtained from a Green's function calculated by exact diagonalization, while the rest is taken into account by a perturbative treatment. With this method the band structure of LiH is calculated and reasonable agreement with experiment is found.

DOI
10.1143/jpsj.70.1035

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A local-orbital based ab initio approach to calculate correlation effects on quasi particle energies in insulating solids is presented. The use of localized Wannier-type Hartree Fock orbitals allows to efficiently devide correlation effects into classes of strong, medium or small weight. Subsequently the strongly contributing correlations are obtained from a Green's function calculated by exact diagonalization, while the rest is taken into account by a perturbative treatment. With this method the band structure of LiH is calculated and reasonable agreement with experiment is found.
We present a wave-function-based approach to correlated ab initio calculations on crystalline insulators of infinite extent. It uses the representation of the occupied and the unoccupied (virtual) single-particle states of the infinite solid in terms of Wannier functions. Electron correlation effects are evaluated by considering virtual excitations from a small region in and around the reference cell, keeping the electrons of the rest of the infinite crystal frozen at the Hartree-Fock level. The method is applied to study the ground-state properties of the LiH crystal and is shown to yield rapidly convergent results.
We propose a new, alternative method for ab-initio calculations of the electronic structure of solids, which has been specifically adapted to treat many-body effects in a more rigorous way than many existing ab-initio methods. We start from a standard band-structure calculation for an effective one-particle Hamiltonian approximately describing the material of interest. This yields a suitable set of one-particle basis functions, from which well localized Wannier functions can be constructed using a method proposed by Marzari and Vanderbilt. Within this (minimal) basis of localized Wannier functions the matrix elements of the non-interacting (one-particle) Hamiltonian as well as the Coulomb matrix elements can be calculated. The result is a many-body Hamiltonian in second quantization with parameters determined from first principles calculations for the material of interest. The Hamiltonian is in the form of a multi-band Hamiltonian in second quantization (a kind of extended, multi-band Hubbard model) such that all the standard many-body methods can be applied. We explicitly show how this approach can be solved in the simplest many-body approximation, the mean-field Hartree-Fock approximation (HFA), which takes into account exact exchange and corrects for self-interaction effects.
Three different many-body wave-function-based ab initio methods for the calculation of correlated (or quasi-particle) band structures of periodic systems are presented: the local Hamiltonian approach, the incremental self-energy method, and the crystal orbital variant of the algebraic diagrammatic construction. All three methods explicitly exploit the local nature of electron correlation, and by consequently switching to representations in localized Wannier orbitals O(N) scaling could be achieved in all three cases. These methods were applied to single (HF) 2 zigzag chains as found in solid hydrogen fluoride using the same geometries and basis sets. Essentially identical quasi-particle band structures were obtained, corroborating the appropriateness of the different concepts pursued in each of the presented quantum chemical correlation methods for band structures of infinite systems.
In this paper we present an approach aimed at performing many-body calculations of Born-effective charges of crystalline insulators by including the electron-correlation effects. The scheme is implemented entirely in the real space, using Wannier functions as single-particle orbitals. Correlation effects are computed by including virtual excitations from the Hartree-Fock mean field, and the excitations are organized as per a Bethe--Goldstone-like many-body hierarchy. The results of our calculations suggest that the approach presented here is promising.
Electronic structure of materials from first principles is essential for one-to-one comparisons between theories and experiments. However, the many-body effects resulting from electron correlation and their interplay with other degrees of freedom pose a great challenge to design an ab initio approximate method with good accuracy and efficiency at the same time. In this thesis, we present our recent developments of ab initio many-body theory for solids based on the finite-temperature Green’s function formalism. We begin by reviewing the basic concepts and definitions of realistic electronic Hamiltonians (Ch. 2) as well as Green’s functions at finite temperature (Ch. 3). Overviews of self-consistent many-body perturbation theories and quantum embedding theories are then presented in Chs. 4 and 5 as complementary materials for the following chapters. In Ch. 6, we present algorithms and implementation details for the finite-temperature self-consistent GW (scGW) method in Gaussian-type orbitals for solids. Our implementation is based on the finite-temperature Green’s function formalism in which all equations are solved on the imaginary axis, without resorting to analytical continuation during the self-consistency. No quasiparticle approximation is employed and all matrix elements of self-energies are explicitly evaluated. We show agreement with other, differently formulated finite-temperature scGW implementations. By migrating computationally intensive calculations to GPUs, we obtain scalable results on large supercomputers with nearly optimal performance. Inclusion of relativistic effects in scGW is discussed in Ch. 7. Our formulation of relativistic scGW is based on the exact two-component formalism with one-electron approximation (X2C1e) and non-relativistic Coulomb interactions. Our theory allows us to study scalar relativistic effects, spin-orbit coupling, and their interplay with electron correlation without adjustable parameters. We examine the effect of the X2C1e by comparison to the established four-component formalism and reach excellent agreement. The simplicity of X2C1e enables construction of higher order theories, such as embedding theories, on top of perturbative calculations. In Ch. 8, we use self-energy embedding theory (SEET) to study the spectra of the prototypical undistorted cubic perovskites SrVO3 and SrMnO3. In the strongly correlated metallic SrVO3, we find that the usual attribution of the satellite peaks at -1.8 eV to Hund or Hubbard physics in the t2g orbitals is inconsistent with our calculations. In the strongly correlated insulator SrMnO3 we recover insulating behavior due to a feedback effect between the strongly correlated orbitals and the weakly correlated environment. Our calculation shows a systematic convergence of spectral features as the space of strongly correlated orbitals is enlarged, paving the way to a systematic parameter-free study of correlated perovskites. Lastly, in Ch. 9, we apply the Green’s function coupled cluster singles and doubles (GFCCSD) impurity solver to realistic impurity problems in strongly correlated solids within the framework of SEET. We describe the implementation details of our Green’s function coupled cluster (GFCC) solver, investigate its performance, and highlight potential advantages and problems on examples of impurities created for antiferromagnetic MnO and paramagnetic SrMnO3. GFCCSD provides satisfactory descriptions for weakly and moderately correlated impurities with sizes that are intractable by existing accurate impurity solvers such as exact diagonalization. However, when correlations become strong, the singles and doubles approximation used in GFCC could lead to instabilities in searching for the particle number present in impurity problems.