downfolding and LDA+DMFT

[SimonLi]

Dear all

As a new user of abinit, I have a few questions concerning the usage of the LDA+DMFT interface. The central question is actually simple, how can I get the band structure of an interacting system from LDA+DMFT. These concern a few more detailed questions, which may help you to get what I really want to know. The general logic of abinit LDA+DMFT calculations seems to be the following: For a given interacting system, by specifying the band indices and atomic orbital characters to abinit, abinit projects the Bloch bands to a hamiltonian with dimension of the # of orbitals specified. Then, this Hamiltonian is solved in DMFT by certain impurity solver. The standard output of the entire LDA+DMFT calculations is the impurity self-energy. Now, my questions are

(1). How can one tell the quality of projection? Is there any way to visualize the projected band structure and compare them to the original Bloch band from, e.g. LDA?
(2). Is it possible to visualize the characters of the projected orbitals from, e.g. the wannier function plot? Plotting the orbital basis functions in real-space would be a straightforward way to understand their characters. In another projection scheme based on the so-called Maximally Localized Wannier Functions, one can plot the MLWFs to get a feeling of the orbital nature. I am looking for something similar to help me to understand the resulting orbital basis functions. Can the same plot be done in Abinit?
(3). I am very interested in the electronic structure plot in the LDA+DMFT calculations. As far as I understand, I need two ingredients: the projected LDA band structure (the"non-interacting" Hamiltonian in LDA+DMFT) and the DMFT local self-energy. The latter is a standard output of the impurity solvers. I am wondering, how the former, i.e. projected LDA band, can be obtained from the interface? Where are they stored, or is there any script that can help me to generate them? This should not be of principle problem as, in any case, it is also an input to the DMFT circle.

I would be very thankful to you guys for valuable explanations.
Gang Li
University of Wuerzburg
Germany

[amadon]

Dear SimonLi,

First, could you kindly precise your name and affiliation as a presentation ? Thanks !

The DFT+DMFT implementation in ABINIT is mainly oriented towards energy calculations. There are no direct ways easily available in ABINIT
to compute the band structure in DFT+DMFT. As explained in the input variable usedmft and related variable, the partial and total spectral function can be computed with the Hubbard I solver. With QMC, the local Green's function in imaginary time is produced and thus the calculation of electronic structure requires an analytical continuation (not yet distributed in ABINIT).

(1) The question is what is quality ? Numerically, the projections are tested and thus accurately computed. Physically, they rely on a window of energy. Depending on this window, the definition of correlated orbitals change and thus the band structure on the Wannier basis. A detailed explanation of these effects can be found in Phys. Rev. B 77, 205112 (2008) and related papers. The projected band structure will soon be available.

(2) This is not yet possible to plot Wannier functions as constructed in ABINIT in the DFT+DMFT scheme. However, please note that if one is interested in e.g d orbitals (lpawu=2), thus Wannier projected d-orbitals can only be by construction d-orbitals. The orbital nature is thus well defined. As you precise, for MLWF, this is not the case because the minimization scheme can lead to a change of the character.

(3) Electronic structure plot cannot be obtained straighforwardly (with band structure and self-energy) because the calculation is made with imaginary frequency thus computing the electronic structure would require an analytical continuation. This is not yet distributed in ABINIT.

Best regards
Bernard Amadon

[SimonLi]

Dear Amadon

Thank you for your reply. A bit more information about myself has been added as requested.

(1) By quality, I meant that the projected bands (with e.g. only d-orbital) are expected to be well on top of the corresponding Bloch bands from DFT. Thus, if the projected bands can be plotted against the DFT bands, the quality of projection can be easily visualized. This is the case for the MLWFs scheme, where one can plot both in one figure for comparison. I am not saying MLWFs is better in this sense, I only use it as an example to let you get what I meant by quality. Is there any way that I can plot the projected band structure from abinit, as this also relates to my question about the band structure in LDA+DMFT, which I specify also in (3)

(2) this is clear now, I guess in abinit the initial orbital does not change in the downfolding procedure, they remain to be the perfect atomic form. Thank you.

(3) I am also working on CT-QMC for models and LDA for materials, but I have not yet implemented my own code to combine them to perform LDA+DMFT full charge self-consistent calculations, probably I will never do that if I am able to work with abinit. Thus, analytical continuation is not a problem to me. The only thing bothers me is that: in order to calculate A(k, w) which is the electronic structure with the presence of interaction, only the local real-frequency self-energy Sigma(w) is not enough, I also need the projected non-interacting dispersion e(k) used in LDA+DMFT.

Code: Select all

A(k,w) = -1/pi Im(1/(w+i*delta + mu - e(k) - Sigma(w))), where delta is an infinitesimal.

My question is how do I get e(k) from abinit? This must be a very simple question to you, as it is used extensively in the DMFT self-consistently procedure. This question is basically same as (1), that how can I read out the projected band dispersion e(k) from abinit?

thank you for any explanation,
Gang