Correction of dielectric shielding for scissor operator

[Quxiao]

Dear developers：
Firstly, I would like to express my sincere gratitude for your continuous assistance. Through your help, I have gained a deeper understanding of Yambo.
My recent concern is that when solving BSE using the scissor operator, two modifications are needed. They are% KfnQP_S and% XfnQP_S, respectively. My understanding is that the first parameter is equivalent to a direct
translation on the single electron energy level, which will affect the single electron energy gap when constructing BSEkernel: \ epsilon-c - \ epsilon-v. The second parameter should affect W. Here, my simple understanding is
that the Coulomb interaction W is approximately related to the single electron energy gap.

But I want to know how Yambo applies the parameter% XfnQP_S to the BSE solving process, is it just a value of W, or is there any corresponding formula? Because the values of% KfnQP_S and% XfnQP_S are both set to
the same translation scissor, I speculate that it may be due to the invariance of BSEkernel's diagonal elements? Keep the value of \ epsilon-ck-epsilon-vk '- W-kk' unchanged?

I would greatly appreciate it if you could explain and let me know if this operation is in a certain Fortran file.

I hope the Yambo team continues to do better and better！
Best wishes!
Quxiao

[Daniele Varsano]

Dear Quxiao,

the scissor operator is applied by setting KfnQP_E and XfnQP_E in the BSE diagonal part or in the screening respectively.
The scissor operator is applied by shifting the all the conduction bands of the given quantity with respect to the maximum valence band.
When applied to W, the independent particle response Xo is calculated using shifted energies and the Dyson equation is solved: this will give a smaller screening with respect to the one calculated with Kohn Sham energies.
Anyway, the usual procedure is to apply the scissor operator to the diagonal part of the kernel to mimic quasiparticle correction and leave the screening calculated with KS energies as it somehow mimic excitation energies, and usually gives more accurate results, unless you want to apply some sort of eigenvalue self-consistency in GW calculation to both G and W.

Best,
Daniele

[Quxiao]

Dear Daniele:
Thank you very much for your reply. I have a better understanding of the operation process of Yambo, but I am still very interested in the specific physical form of the scissor operator. How to construct the scissor operator using KfnQP_S and XfnQP_S, and what is the specific physical form, such as scissor operator=f (KfnQP_S, XfnQP_S), what is the specific form of f? This will facilitate my deeper understanding of physical images.
Thanks again!
Best wishes!
Quxiao

[Daniele Varsano]

Dear Quxiao,

please note, the name of the variable is KfnQP_E and not KfnQP_S.
For example:

Code: Select all

% KfnQP_E
 2.000000 | 1.100000 | 1.100000 |         # E parameters  (c/v) eV|adim|adim
%

The form of the operator is a constant scissor (open of the gap) given by the first number (here 2.0eV) and a linear stretching of the conduction and valence band given by the slope in input (second and third entry).

The same for the XfnQP_E but applied to the response function X.

Best,
Daniele

[Quxiao]

Dear Daniele:
I'm very sorry, I made a mistake by typing the wrong variable. I know for sure that it changed KfnQP_E and XfnQP_E,But I would rather know how XfnQP_E affects the response function X and ultimately affects the W matrix, which is more urgent for me to clarify. If you have a clearer physical formula, please help me understand. Thank you!
Best Wishes!
Quxiao

[Daniele Varsano]

Dear Quixiao,
you can have a look at the calculation of the independent particle polarizability:
see. Eq. 3 of the Yambo cheatsheet: https://www.yambo-code.eu/wiki/images/c ... et-5.0.pdf

XfnQP_E applies a scissor to the energy difference entering in Xo, so that you will have Ec - Ev+Delta.
The effect is that the larger the scissor, the larger the gap and consequently the screening will be lowered and W enhanced.

Best,
Daniele