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TRIQS/DFTTools: A TRIQS application for ab initio calculations of correlated materials
Markus Aichhorn, Leonid Pourovskii, Priyanka Seth, Veronica Vildosola, Manuel Zingl, Oleg E. Peil, Xiaoyu Deng, Jernej Mravlje, Gernot J. Kraberger, Cyril Martins, Michel Ferrero, Olivier Parcollet
TL;DR
Correlated materials can fall outside standard DFT and band-theory descriptions, motivating computational tools that combine DFT with dynamical mean-field theory. TRIQS/DFTTools provides Wannier construction, DMFT self-consistency, DFT interfaces, charge self-consistency through Wien2k, and post-processing for calculated physical properties. Its scope is bounded by the lack of built-in analytic continuation and the Wien2k requirement for full charge self-consistency.
Problem
Standard DFT and band theory cannot describe correlation-driven insulating behavior in some partially filled d- and f-shell materials, while correlated metals require dynamical many-body effects.
Method
TRIQS/DFTTools connects DFT calculations to Python DMFT modules through projective Wannier functions, with Wien2k and generic interfaces.
Results
The package provides charge self-consistent Wien2k calculations, broader DFT or tight-binding interfaces, and tools for spectral, density-of-states, optical, thermoelectric, and transport properties.
Takeaways & Limitations
TRIQS/DFTTools supplies a complete implementation framework for ab initio correlated-material calculations and subsequent analysis of experimentally connected physical properties.
Takeaways & Limitations
TRIQS/DFTTools does not provide analytic continuation, and only the Wien2k interface enables fully charge self-consistent calculations requiring Wien2k knowledge.
Abstract
from arXiv · showhide
We present the TRIQS/DFTTools package, an application based on the TRIQS library that connects this toolbox to realistic materials calculations based on density functional theory (DFT). In particular, TRIQS/DFTTools together with TRIQS allows an efficient implementation of DFT plus dynamical mean-field theory (DMFT) calculations. It supplies tools and methods to construct Wannier functions and to perform the DMFT self-consistency cycle in this basis set. Post-processing tools, such as band-structure plotting or the calculation of transport properties are also implemented. The package comes with a fully charge self-consistent interface to the Wien2k band structure code, as well as a generic interface that allows to use TRIQS/DFTTools together with a large variety of DFT codes. It is distributed under the GNU General Public License (GPLv3).
PROGRAM SUMMARY
TRIQS/DFTTools is a Unix/Linux/OSX application distributed through GitHub under GPLv3, with problem-dependent resource requirements and runtime.
- TRIQS/DFTTools runs on Unix, Linux, and OSX systems across architectures with suitable compilers, including PCs and clusters.
- The package is distributed through GitHub as a downloadable zip under the GNU General Public License (GPLv3).
- Test runs take less than a minute, while other running times are highly problem dependent.
1. Introduction and Motivation
The paper motivates DFT+DMFT for correlated materials where standard DFT and band theory can fail, and presents TRIQS/DFTTools as a comprehensive implementation package.
- Standard DFT uses Kohn-Sham equations to obtain orbitals and energies, but relies on approximate exchange-correlation potentials.
- Band theory can fail for partially filled d- and f-shell compounds, where DFT predicts metals but experiments show correlation-driven insulating behavior.
- DFT+DMFT combines the non-local quantum Hamiltonian from DFT with local quantum correlations to describe correlated materials.
- Numerical advances have enabled more accurate ab initio studies of realistic materials at experimentally relevant ambient and lower temperatures.
- TRIQS/DFTTools provides charge self-consistent Wien2k coupling, broader DFT or tight-binding interfaces, physical-property calculations, spin polarization, spin-orbit coupling, and GPLv3 licensing.
- The paper introduces projective Wannier functions and presents examples, post-processing tools, installation information, and concluding material.
2. General structure of TRIQS/DFTTools
TRIQS/DFTTools connects DFT outputs to Python-based DMFT modules through Wannier representations and supports analysis of calculated observables.
- Python modules implement the DMFT self-consistency cycle, while DFT-dependent interfaces provide the required electronic-structure input.
- Only the Wien2k interface supports fully charge self-consistent calculations; the generic interface supports other codes without that capability.
- After DFT, Kohn-Sham orbitals are converted into localized Wannier orbitals and required information is stored in an HDF5 file for DMFT.
- Analysis tools include spectral functions, densities of states, and transport properties, with analytic continuation potentially required for some impurity solvers.
3. The interface to DFT
TRIQS/DFTTools constructs projective Wannier functions from DFT bands and converts the resulting information into a format usable for DMFT. Its interfaces support charge-self-consistent Wien2k calculations and more general Wannier-based inputs, while projection-window choices affect Wannier localisation.
- 3.1. Projective Wannier functions: Projective Wannier functions are constructed by expanding local orbitals over Bloch bands within an energy window and orthonormalising them.The resulting Bloch-transformed functions provide the localised basis used for DMFT calculations.
- 3.1. Projective Wannier functions: Projection operators transform quantities from the Bloch-band basis to the Wannier-orbital basis and support calculation of projected local Green’s functions.The projectors are used to obtain the local projected non-interacting Matsubara Green’s function from the DFT Green’s function.
- 3.1. Projective Wannier functions: In SrVO3, enlarging the projection window from vanadium t2g bands to include oxygen p bands produces better-localised d-like Wannier functions.Using an even larger window changes the DOS mainly through a small transfer of weight around 7 eV.
- 3.2. Interface to Wien2k: The dmftproj program extracts Wien2k data, computes projection-operator matrix elements, and gathers the Hamiltonian, coordinate rotations, and symmetry matrices needed for DMFT.The workflow begins with a self-consistent Wien2k calculation and stores the resulting information in a single hdf5 file.
- 3.3. General interface for non-Wien2k users: The generic interface accepts a correlated-subspace Hamiltonian from Wannier90, NMTO, or another tight-binding representation, but does not provide full charge self-consistency.This interface performs the calculation exclusively in Wannier-orbital space and is independent of how the Hamiltonian was produced.
4. One-shot DFT+DMFT calculations
One-shot DFT+DMFT calculations use compact Python modules to iterate the self-consistency cycle from a prepared hdf5 archive. The cycle updates the self-energy, chemical potential, local Green’s function, hybridisation, impurity solution, and double-counting correction until convergence.
- 4. One-shot DFT+DMFT calculations: The one-shot workflow initializes SumkDFT with an hdf5 archive, creates an impurity solver, and iterates a user-defined number of DMFT loops.The example script illustrates calculations without full charge self-consistency.
- 4. One-shot DFT+DMFT calculations: Each iteration sets the impurity self-energy, determines the chemical potential for the required density, and calculates the local Green’s function.The self-energy is represented in orbital space, while the required density is defined within the projection window.
- 4. One-shot DFT+DMFT calculations: The updated Weiss field is obtained through the Dyson equation, after which the chosen solver produces the interacting impurity Green’s function and self-energy.The solver and its parameters must be selected appropriately to obtain meaningful and physically sound results.
- 4. One-shot DFT+DMFT calculations: A new double-counting correction is calculated from the impurity density matrix using the Hubbard interaction U, Hund’s exchange J, and a selected correction formula.TRIQS/DFTTools offers three double-counting corrections, including the fully localised limit correction.
- 4. One-shot DFT+DMFT calculations: Steps one through six are iterated until convergence, after which the final Green’s function and self-energy can be saved in the hdf5 archive.The paper emphasizes that the complete calculation can be implemented in about 30 lines of Python code.
5. Full charge self-consistency
TRIQS/DFTTools extends the Wien2k self-consistency loop with a DMFT step that incorporates correlation-corrected charge densities. Fully charge self-consistent calculations require Wien2k knowledge but generally add about 50% computational effort and enable total-energy calculations.
- Concept and interface: The one-shot DFT+DMFT calculation can be extended to full charge self-consistency with only marginal additional effort.The implementation described targets the Wien2k DFT package.
- Self-consistency cycle: The charge self-consistent loop supplements the DFT charge density from Kohn-Sham orbitals with correlation effects from a DMFT step.The existing Wien2k self-consistency cycle is extended rather than replaced.
- Convergence: One DMFT iteration per full self-consistency cycle is usually sufficient, although problematic convergence may require more iterations.The prescribed iteration count is therefore a practical default rather than a universal rule.
- Charge correction: The correlated density matrix is calculated from the Green’s function and used instead of the Kohn-Sham density matrix to obtain the charge density.Relevant properties are saved in the hdf5 archive for the next iteration.
- Cost and capabilities: Around 50% additional computational effort is normally required because fully charge self-consistent calculations use more self-consistency loops.The actual overhead depends on the problem and on whether DMFT charge-density corrections matter.
- Cost and capabilities: The charge self-consistent implementation also allows total energies to be calculated from DFT+DMFT.Detailed formulas and their derivation are cited in the paper.
6. Post-processing
TRIQS/DFTTools post-processes DMFT outputs to produce quantities more directly connected to experimental observables, including density of states, transport properties, and optical conductivity. These analyses require a real-frequency self-energy, obtained by analytic continuation when necessary.
- Purpose: TRIQS/DFTTools processes the interacting Green’s function and self-energy to calculate physical properties connected to experimental observables.The package includes methods for further processing DMFT data.
- Available quantities: Post-processing includes orbitally projected density of states.
- Available quantities: Post-processing includes resistivity, thermopower, and optical conductivity.
- Frequency representation: A real-frequency self-energy is required for these methods; Matsubara-axis data must be analytically continued when the solver provides no real-frequency result.The paper lists Padé approximants and maximum entropy among possible continuation methods.
DOS and band structure.
The package computes correlated band structures and local spectral functions from real-frequency Green’s functions in a Wannier-based representation. For SrVO3, DMFT renormalizes the t2g bands while affecting oxygen p and vanadium eg states only marginally.
- Method: The band-structure Green’s function uses a real-frequency self-energy, and summing the traced quantity over the first Brillouin zone gives the local spectral function.
- SrVO3 setup: For SrVO3, the comparison uses projective Wannier functions over the [−8.5, 7.5]eV window and stochastic maximum entropy for analytic continuation.The impurity problem uses U = 6.0 eV and J = 0.65 eV with the TRIQS/CTHYB solver.
- SrVO3 results: The t2g bands show mass renormalisation smaller than 2, whereas oxygen p and vanadium eg states are only marginally affected.
- SrVO3 results: Hybridisation between vanadium t2g and oxygen p states gives the bands between −7 and −2 eV a finite width.
- Figure comparison: Figure 5 compares correlated and DFT band structures on the left and correlated local spectral functions with DFT DOS on the right.
Transport properties.
TRIQS/DFTTools evaluates transport coefficients using Kubo linear response, spectral functions, band velocities, and real-frequency self-energies. For SrVO3, calculated resistivity, Seebeck coefficient, and optical conductivity compare reasonably with experiment, subject to stated approximations and convergence requirements.
- Method: Transport calculations use Kubo linear response, neglect vertex corrections, and require band velocities from Wien2k optics matrix elements.
- Method: The transport distribution combines velocity matrices with spectral-function matrices in the band indices.In multiband systems, both velocities and spectral functions are Hermitian matrices.
- SrVO3 results: For SrVO3 at 290 K, the calculated DC resistivity is 47 µΩcm versus an experimental value of 70 µΩcm.The calculation uses 4495 k-points in the irreducible Brillouin zone.
- SrVO3 results: The calculated Seebeck coefficient is −8 µV/K, compared with an experimental room-temperature value of about −11 µV/K.
- SrVO3 results: DFT+DMFT optical conductivity is compared with both direct DFT conductivity and experimental data.The comparison is shown for SrVO3 in Figure 6.
- Caveats: When phonons, impurities, or non-local fluctuations are omitted, the calculated resistivity constitutes a lower bound to the expected experimental value.Transport convergence with respect to the number of k-points must be checked carefully.
7. Getting started
TRIQS/DFTTools is publicly available through GitHub, with installation supported by CMake after TRIQS is installed. Users can choose current development sources or a stable tagged release, and contribute feedback or code through the project’s channels.
- Code distribution: GitHub provides the public source code, current updates, bugfixes, and tagged releases.The latest GitHub source is recommended for ongoing improvements, while tagged releases offer greater stability without the newest changes.
- Installation: Installation uses CMake to configure, build, test, and install TRIQS/DFTTools after the TRIQS library is properly installed.The documented commands clone the source, create a build directory, configure with TRIQS_PATH, compile, run tests, and install.
- Usage and contribution: Published users are asked to cite TRIQS/DFTTools, its original implementation and charge-self-consistency works, the TRIQS library, and any solver used.The paper also directs users to report issues through GitHub and coordinate major contributions with the developers.
8. Summary
The paper presents TRIQS/DFTTools as a TRIQS-based application for setting up DFT+DMFT calculations. Examples demonstrate calculations of Wannier functions, spectral functions, and transport properties for SrVO3.
- Summary: TRIQS/DFTTools provides the tools needed to set up DFT+DMFT calculations.The package is presented as an application based on the TRIQS library.
- Summary: Examples demonstrate calculations of Wannier functions, spectral functions, and transport properties for SrVO3.These examples illustrate how the package can be used for a prototypical material.