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Charge self-consistent electronic structure calculations with dynamical mean-field theory usingQuantum ESPRESSO, Wannier 90andTRIQS

Sophie Beck, Alexander Hampel, Olivier Parcollet, Claude Ederer, Antoine Georges

Published Jun 8, 2022• 22 citations
Publisher

Abstract

We present a fully charge self-consistent implementation of dynamical mean field theory (DMFT) combined with density functional theory (DFT) for electronic structure calculations of materials with strong electronic correlations. The implementation uses theQuantum ESPRESSOpackage for the DFT calculations, theWannier90code for the up-/down-folding and theTRIQSsoftware package for setting up and solving the DMFT equations. All components are available under open source licenses, are MPI-parallelized, fully integrated in the respective packages, and use an hdf5 archive interface to eliminate file parsing. We show benchmarks for three different systems that demonstrate excellent agreement with existing DFT + DMFT implementations in otherab initioelectronic structure codes.

DOI
10.3929/ethz-b-000543431

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We present a fully charge self-consistent implementation of dynamical mean field theory (DMFT) combined with density functional theory (DFT) for electronic structure calculations of materials with strong electronic correlations. The implementation uses theQuantum ESPRESSOpackage for the DFT calculations, theWannier90code for the up-/down-folding and theTRIQSsoftware package for setting up and solving the DMFT equations. All components are available under open source licenses, are MPI-parallelized, fully integrated in the respective packages, and use an hdf5 archive interface to eliminate file parsing. We show benchmarks for three different systems that demonstrate excellent agreement with existing DFT + DMFT implementations in otherab initioelectronic structure codes.
We present a new open-source program, DCore, that implements dynamical mean-field theory (DMFT). DCore features a user-friendly interface based on text and HDF5 files. It allows DMFT calculations of tight-binding models to be performed on predefined lattices as well as ab initio models constructed by external density functional theory codes through the Wannier90 package. Furthermore, DCore provides interfaces to many advanced quantum impurity solvers such as quantum Monte Carlo and exact diagonalization solvers. This paper details the structure and usage of DCore and shows some applications.
ComDMFT is a parallel computational package designed to study the electronic structure of correlated quantum materials from first principles. Our approach is based on the combination of first-principles methods and dynamical mean field theories. In version 2.0, we implemented fully-diagrammatic GW+EDMFT from first-principles. In this approach, correlated electrons are treated within full GW+EDMFT and the rest are treated within full-GW, seamlessly. This implementation enables the electronic structure calculation of quantum materials with weak, intermediate, and strong electron correlation without prior knowledge of the degree of electron correlation.
Strongly correlated systems are a class of materials whose electronic structure is heavily influenced by the effect of electron-electron interactions.In these systems, an effective singleparticle description may not capture the many-body effects accurately.Although density functional theory (DFT) plus dynamical mean-field theory (DMFT) has proven successful in describing strongly correlated electron systems for over two decades, only very recently ready-to-use software packages have begun to become available, with most scientific research carried out by in-house codes developed and used in individual research groups.Given the complexity of the method, there is also the question of whether users should implement the formalism themselves for each problem or whether black-box software, analogous to popular DFT packages, would be beneficial to the community.
The convergence to the self-consistency in the dynamical mean-field theory (DMFT) calculations for models of correlated electron systems can be significantly accelerated by using an appropriate mixing of hybridization functions which are used as the input to the impurity solver. It is shown that the techniques and the past experience with the mixing of input charge densities in the density-functional theory calculations are also effective in DMFT. As an example, the increase in the computational requirements near the Mott metal-insulator transition in the Hubbard model due to critical slowing down can be strongly reduced by using the modified Broyden's method to numerically solve the nonlinear self-consistency equation. Speed-up factors as high as three were observed in practical calculations even for this relatively well-behaved problem. Furthermore, the convergence can be achieved in difficult cases where simple linear mixing is either not effective or even leads to divergence. Unstable and metastable solutions can also be obtained. We also determine the linear response of the system with respect to the variations in the hybridization function, which is related to the propagation of the information between the different energy scales during the iteration.
Dynamical Mean-Field Theory (DMFT) has opened new perspectives for the investigation of strongly correlated electron systems and greatly improved our understanding of correlation effects in models and materials. In contrast to Hartree-Fock-type approximations the mean field of DMFT is dynamical, whereby local quantum fluctuations are fully taken into account. DMFT becomes exact in the limit of high spatial dimensions or coordination number. Using DMFT the dynamics of correlated electron systems can be investigated non-perturbatively at all interaction strengths, electron densities and temperatures. By merging density functional theory with DMFT a powerful method for the calculation of the properties of correlated electron materials has become available, which is applicable to bulk systems and heterostructures, including topological states of matter. The inclusion of non-local correlations into DMFT makes it possible to explore unconventional superconductivity and the critical behavior at thermal or quantum phase transitions. By generalizing DMFT to non-equilibrium states also the real-time dynamics of correlated systems can be investigated. In this brief review the foundations and current status of DMFT are discussed along with characteristic physical insights obtained with this approach.
Abstract This article is a short introduction to the modern computational techniques used to tackle the many-body problem in materials. The aim is to present the basic ideas, using simple examples to illustrate strengths and weaknesses of each method. We will start from density-functional theory (DFT) and the Kohn–Sham construction—the standard computational tools for performing electronic structure calculations. Leaving the realm of rigorous density-functional theory, we will discuss the established practice of adopting the Kohn–Sham Hamiltonian as approximate model. After recalling the triumphs of the Kohn–Sham description, we will stress the fundamental reasons of its failure for strongly-correlated compounds, and discuss the strategies adopted to overcome the problem. The article will then focus on the most effective method so far, the DFT+DMFT technique and its extensions. Achievements, open issues and possible future developments will be reviewed. The key differences between dynamical (DFT+DMFT) and static (DFT+ U ) mean-field methods will be elucidated. In the conclusion, we will assess the apparent dichotomy between first-principles and model-based techniques, emphasizing the common ground that in fact they share.