Introduction

This site collects first-principles calculations of strongly correlated materials, computed with density functional theory combined with dynamical mean field theory (DFT + DMFT). This page explains the method briefly, what each quantity in the database means, and where to learn more.

What is DFT + DMFT?

Density functional theory describes many materials very well, but it fails when electrons in partially filled d or f shells interact strongly. Examples are Mott insulators, heavy-fermion metals, Hund's metals and the actinides. Dynamical mean field theory treats these local interactions exactly by mapping the solid onto a single atom embedded in a self-consistently determined electronic bath. Combining the two gives a first-principles method that captures both band formation and atomic-like physics: quasiparticle renormalisation, Hubbard bands, local moments and valence fluctuations.

The embedded DMFT functional (eDMFT)

The W2K database was computed with the embedded DMFT functional, eDMFT, developed by Kristjan Haule on top of the Wien2K code. Correlated orbitals are defined by projection inside the muffin-tin spheres, the double counting is treated exactly, and the method is charge self-consistent and gives total energies and forces. The impurity problems are solved with continuous-time quantum Monte Carlo (CTQMC) or with the OCA/NCA solvers.

The LMTO database contains earlier LDA+DMFT results obtained with the LMTO method (LmtART). The eDMFT code itself is free to download from the Downloads page.

What the plots show

Each compound in the database has a page per quantity. The examples below open a live plot.

Density of states (DOS)

The number of electronic states per energy, in total and projected on atoms and orbitals (s, p, d, f). Peaks away from the Fermi level (E = 0) are often Hubbard bands; a narrow peak at E_F signals heavy quasiparticles. Example: Am

Spectral function A(k,ω)

The momentum-resolved DOS along a path through the Brillouin zone: the correlated counterpart of a band structure, directly comparable with angle-resolved photoemission (ARPES). Broad, faint features show strong scattering. Example: Am (interactive), FeSe

Self-energy Σ(ω)

Describes how correlations modify the electrons. On the real axis, the slope of Re Σ at ω = 0 gives the mass enhancement m*/m = 1 − ∂Re Σ/∂ω, and −Im Σ is the scattering rate. One curve is shown for each independent orbital component (for example t_2g and e_g). Example: AmC

Local Green's function G and hybridization Δ

The quantities of the auxiliary impurity problem that DMFT solves self-consistently: G is the local propagator of the correlated orbitals, Δ describes how they exchange electrons with the rest of the solid. Example: FeSe Δ

Valence histogram

The probability of each atomic configuration of the correlated ion, sampled by CTQMC: the probability of finding N electrons in the shell, and of each individual atomic state. A broad distribution means strong valence fluctuations (mixed valence). Example: URu2Si2, Pu

Optical conductivity σ(ω)

The response to light, comparable with infrared and optical spectroscopy. Curves are labelled by polarisation (σ_xx, σ_zz, in-plane average …). Example: URu2Si2, BaFe2As2

LDA DOS, LDA optics, bands

The same quantities from plain DFT, the uncorrelated reference. Comparing them with the DMFT results shows what correlations change. Example: LaNiO3, CmC bands with orbital character

Imaginary (Matsubara) axis

Many calculations, in particular those with the CTQMC solver, are performed at imaginary frequencies iω_n = (2n+1)πT. Such data needs no analytic continuation and carries only the statistical error of the solver, but it is not directly a spectrum; the site labels it as such. In a Fermi liquid −Im Σ(iω_n) is linear at low frequency, −Im Σ ≈ (1/Z − 1) ω_n, where Z = m/m* is the quasiparticle weight. Example: FeSe

Using the site

• Open a compound from the W2K or LMTO table. Greyed entries are not available for that compound.
• In a plot, drag to zoom, double-click to reset, click legend entries to hide curves, or type exact limits. The address bar keeps your selection, so you can share a link to exactly what you see.
• Download CSV saves the plotted numbers; download data packs the input and result files of a compound into one archive, ready to start a new calculation.
• The input generator builds params.dat and sparams.dat for a new LDA+DMFT run, starting from any LMTO compound.
• The documentation pages (W2K, LMTO) list which files each plot is made from.

Learn more

The tutorials teach eDMFT step by step. Several of them treat materials that are in the database, so you can compare your own run with the stored result:

Lectures on DFT + DMFT and the source code are on the Downloads page.

How to cite

If you use results or the code from this site, please cite the methods papers:

• G. Kotliar, S. Y. Savrasov, K. Haule, V. S. Oudovenko, O. Parcollet and C. A. Marianetti, Electronic structure calculations with dynamical mean-field theory, Rev. Mod. Phys. 78, 865 (2006).
• K. Haule, C.-H. Yee and K. Kim, Dynamical mean-field theory within the full-potential methods: Electronic structure of CeIrIn₅, CeCoIn₅, and CeRhIn₅, Phys. Rev. B 81, 195107 (2010).
• K. Haule, Exact double counting in combining the dynamical mean field theory and the density functional theory, Phys. Rev. Lett. 115, 196403 (2015).
• K. Haule and T. Birol, Free energy from stationary implementation of the DFT+DMFT functional, Phys. Rev. Lett. 115, 256402 (2015).

and, for a particular compound, the paper listed under reference in the W2K table.

Contact

The eDMFT code and this web site are written by Kristjan Haule, Department of Physics and Astronomy, Rutgers University. Questions, corrections and suggestions are welcome: haule@physics.rutgers.edu.

To contribute a calculation, request an account and submit it; it will be added after review.