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Register a new userElectronic Structure Calculations with Dynamical Mean-Field Theory: A Spectral Density Functional Approach
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We present a review of the basic ideas and techniques of the spectral density functional theory which are currently used in electronic structure calculations of strongly-correlated materials where the one-electron description breaks down. We illustrate the method with several examples where interactions play a dominant role: systems near metal-insulator transition, systems near volume collapse transition, and systems with local moments.
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We review the basic ideas of the dynamical mean field theory (DMFT) and some of the insights into the electronic structure of strongly correlated electrons obtained by this method in the context of model Hamiltonians. We then discuss the perspectives for carrying out more realistic DMFT studies of strongly correlated electron systems and we compare it with existent methods, LDA and LDA+U. We stress the existence of new functionals for electronic structure calculations which allow us to treat situations where the single--particle description breaks down such as the vicinity of the Mott transition.
We propose a hybrid approach which employs the dynamical mean-field theory (DMFT) self-energy for the correlated, typically rather localized orbitals and a conventional density functional theory (DFT) exchange-correlation potential for the less correlated, less localized orbitals. We implement this self-energy (plus charge density) self-consistent DFT+DMFT scheme in a basis of maximally localized Wannier orbitals using Wien2K, wien2wannier, and the DMFT impurity solver w2dynamics. As a testbed material we apply the method to SrVO$_3$ and report a significant improvement as compared to previous $d$+$p$ calculations. In particular the position of the oxygen $p$ bands is reproduced correctly, which has been a persistent hassle with unwelcome consequences for the $d$-$p$ hybridization and correlation strength. Taking the (linearized) DMFT self-energy also in the Kohn-Sham equation renders the so-called double-counting problem obsolete.
We introduce a spectral density functional theory which can be used to compute energetics and spectra of real strongly--correlated materials using methods, algorithms and computer programs of the electronic structure theory of solids. The approach considers the total free energy of a system as a functional of a local electronic Green function which is probed in the region of interest. Since we have a variety of notions of locality in our formulation, our method is manifestly basis--set dependent. However, it produces the exact total energy and local excitational spectrum provided that the exact functional is extremized. The self--energy of the theory appears as an auxiliary mass operator similar to the introduction of the ground--state Kohn--Sham potential in density functional theory. It is automatically short--ranged in the same region of Hilbert space which defines the local Green function. We exploit this property to find good approximations to the functional. For example, if electronic self--energy is known to be local in some portion of Hilbert space, a good approximation to the functional is provided by the corresponding local dynamical mean--field theory. A simplified implementation of the theory is described based on the linear muffin--tin orbital method widely used in electronic strucure calculations. We demonstrate the power of the approach on the long--standing problem of the anomalous volume expansion of metallic plutonium.
A versatile method for combining density functional theory (DFT) in the local density approximation (LDA) with dynamical mean-field theory (DMFT) is presented. Starting from a general basis-independent formulation, we use Wannier functions as an interface between the two theories. These functions are used for the physical purpose of identifying the correlated orbitals in a specific material, and also for the more technical purpose of interfacing DMFT with different kinds of band-structure methods (with three different techniques being used in the present work). We explore and compare two distinct Wannier schemes, namely the maximally-localized-Wannier-function (MLWF) and the $N$-th order muffin-tin-orbital (NMTO) methods. Two correlated materials with different degrees of structural and electronic complexity, SrVO3 and BaVS3, are investigated as case studies. SrVO3 belongs to the canonical class of correlated transition-metal oxides, and is chosen here as a test case in view of its simple structure and physical properties. In contrast, the sulfide BaVS3 is known for its rich and complex physics, associated with strong correlation effects and low-dimensional characteristics. New insights into the physics associated with the metal-insulator transition of this compound are provided, particularly regarding correlation-induced modifications of its Fermi surface. Additionally, the necessary formalism for implementing self-consistency over the electronic charge density in a Wannier basis is discussed.
Dynamical Mean Field Theory (DMFT) is a successful method to compute the electronic structure of strongly correlated materials, especially when it is combined with density functional theory (DFT). Here, we present an open-source computational package (and a library) combining DMFT with various DFT codes interfaced through the Wannier90 package. The correlated subspace is expanded as a linear combination of Wannier functions introduced in the DMFT approach as local orbitals. In particular, we provide a library mode for computing the DMFT density matrix. This library can be linked and then internally called from any DFT package, assuming that a set of localized orbitals can be generated in the correlated subspace. The existence of this library allows developers of other DFT codes to interface with our package and achieve the charge-self-consistency within DFT+DMFT loops. To test and check our implementation, we computed the density of states and the band structure of well-known correlated materials, namely LaNiO3, SrVO3, and NiO. The obtained results are compared to those obtained from other DFT+DMFT implementations.
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