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Journal of Physics Condensed Matter

Applications of path-integral renormalization group method combined with density functional theory

Yoshiki Imai, Yuichi Otsuka, Masatoshi Imada

Published Aug 24, 2007• 5 citations
Publisher

Abstract

The path-integral renormalization group method is an efficient tool for computing electronic structure of strongly correlated electron systems. Combined with the conventional density functional approaches as a hybrid scheme, it offers a first-principles method for complex materials with involved electron correlation effects. We assess the efficiency and applicability of the hybrid scheme by examining applications to Sr(2)VO(4) and YVO(3).

DOI
10.1088/0953-8984/19/36/365230

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The path-integral renormalization group method is an efficient tool for computing electronic structure of strongly correlated electron systems. Combined with the conventional density functional approaches as a hybrid scheme, it offers a first-principles method for complex materials with involved electron correlation effects. We assess the efficiency and applicability of the hybrid scheme by examining applications to Sr(2)VO(4) and YVO(3).
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.
Path‐integral renormalization‐group (PIRG) method is a rapidly developing tool for computing ground state properties of interacting quantum systems on lattices, particularly models for strongly correlated electrons such as the Hubbard model. It has served in clarifying phase diagrams of the Hubbard model containing quantum spin liquid phase. PIRG has also been implemented as a low‐energy solver of the effective Hamiltonian for realistic systems. This makes it possible to construct a scheme of first‐principles calculation by the hybrid approach combined with the density functional theory.
A variety of quantum many-body methods have been developed for studying the strongly correlated electron systems. We have also proposed a computationally efficient and accurate approach, named the correlation matrix renormalization (CMR) method to address the challenges. The theoretic development and benchmark tests of the CMR method are included in this thesis. Meanwhile, ground state total energy is the most important property of electronic calculations. We also investigated an alternative approach to calculate the total energy, and extended this method for magnetic anisotropy energy of ferromagnetic materials. In addition, another theoretical tool, dynamical mean-field theory on top of the density functional theory, has also been used in electronic structure calculations for an Iridium oxide to study the phase transition, which results from an interplay of the d electrons' internal degrees of freedom.
The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.
The density matrix renormalization group (DMRG) method has already proved itself as a very efficient and accurate computational method, which can treat large active spaces and capture the major part of strong correlation. Its application on larger molecules is, however, limited by its own computational scaling as well as demands of methods for treatment of the missing dynamical electron correlation. In this work, we present the first step in the direction of combining DMRG with density functional theory (DFT), one of the most employed quantum chemical methods with favorable scaling, by means of the projection-based wave function (WF)-in-DFT embedding. On two proof-of-concept but important molecular examples, we demonstrate that the developed DMRG-in-DFT approach provides a very accurate description of molecules with a strongly correlated fragment.