Coulomb cutoff

[Daniele Varsano]

Dear Fabio,
thank you very much, I will have a look at the problem, as soon as I find the time.
It is quite strange you have the 3.3 stamp in the output as you should have "GPL Version 3.4.1".
I will try to reproduce the problem with a 1d system, in the case I will not succeed it would be great if you could post your input files (qe/yambo) if this is not a huge calculations. In this case if you could reproduce the problem using softer parameter in order I can reproduce it easily. Anyway I will first try with a 1D system I have more or less ready, as the problem should be general.

Best,
Daniele

[fabio.caruso]

Dear Daniele,

thanks for looking into this. Please let me know if you need you can reproduce the problem, otherwise I will send you my input files.

Best,
Fabio

[Daniele Varsano]

Dear Fabio,
I have reproduced the problem and looked into it.
It is not a simple bug and the solution it is not straightforward. I try to explain it:
The problem it relates with the definition of the macroscopic epsilon in a non-bulk system.
When dealing with a molecule, the macroscopic epsilon it is not well defined and the meaningful quantity related to the absorption it is the polarizability, alfa.
Alfa it is related to the response function X, or if you want, beside volume normalization factor with eels, and for an infinite volume limit the
absorption (alpha) and the eels do coincide (there is also a paper from the group of Lucia Reining on that).
When dealing with a 1D system, the situation is complicated, as you have a periodic direction while the other direction are finite.
When including the cutoff the head (G=0,q=0) component of the coulomb potential is finite and does not diverge as 1/q^2 anymore and this is the reason of
the destruction of the spectrum you are observing when doing the RPA calculation in G-space. The problem does not appear when you do BSE, as in BSE
you do not calculate the absorption from response function X, but from a modified response X_barra that obeys a Dyson like equation:

Code: Select all

X_barra=X^0+X^0(v_barra)X_barra

where v_barra is the coulomb potential where the head is set to zero (see the RMP of Onida, Rening, Rubio), so the problem does not appear, or better in Hartree
approximation (kernel=v, or exchange only). The term including the head are zero anyway because of the finiteness of the head of the coulomb potential, and in this sense here chi and chi_barra do coincide.
So, what I suggest you, but I would continue to think about it and I hope to modify the code in order to be not misleading, what you should look at when doing
the calculation RPA in gspace using the cutoff is not the o.eps, but o.eel
For a molecule I verified that doing and RPA (LF) calculation and a BSE_like including only exchange with the same parameter (the same physics, just a change of basis),
they do coincide, ie the o.eps of the two calculations are the same without cutoff and the o.eel (G-space) is equal to the o.eps (eh-space) with the cutoff.
Now for the 1D system I do not know if the same is valid, you can have a look. Anyway I'm not sure this is the final story, in a 1D or 2D system, you have plasmons along the periodic direction that should give peaks in the EELS, different from the optical absorption and from this it looks this will be not accessible in the G-space. Finally, this is something that has to be solved, and it need some study, of course suggestion are very welcome.
Best,
Daniele

[fabio.caruso]

Dear Daniele,

thanks for the detailed reply.
If I am not mistaken, BSE with the kernel set to zero (i.e., in the Hartree approximation) should be equivalent to the RPA. Is it possible to switch off completely the BSE kernel in YAMBO? In this case, the RPA and BSE should provide identical dielectric functions and eels (except for numerical differences due to the change of basis). This might allow to get the RPA spectrum with cylidrical cutoff. Otherwise, I will check whether the BSE eels (exchange only) is equivalent to RPA absorption (hopefully the plasmons in 1D systems shouldn't have very high intensity).

Thanks.

Best,
Fabio

[Daniele Varsano]

Hi Fabio,
in order to calculate RPA in BSE formalism you need to set the kernel to Hartree (in the new release), or include the "x" part in the old release.
To have the perfect equivalence you should also consider the coulpling part of the BSE. Of course the same number of bands and Gvectors have to be included.
You can have a try without the cutoff, they should be really the same. When including the cutoff, if I'm not wrong, you should see a correspondence between
the eps(BSE) and the eel(G-space). Note that this should be the absorption in RPA.

Best,
Daniele