Absolute value of the imaginary part of the dielectric function

[Quxiao]

Daniele：
I know that there are three options for BSEmod to choose from, which seem to represent three modes: resonant/retared/coupling. Regarding your previous reply, my understanding is that the difference between retared and resonant is the real part of the response function, but this is very important for the final Does the calculation of the dielectric function of , also have an impact? Because I saw the input of other people in the forum, both resonant and retarted, about the accurate application of these three modes, whether it is displayed in the learn module or other links, maybe due to my negligence, I did not find this introduction. .
Finally, if I calculate the normal BSE, should I choose resonant or retarted? Or both?
Thanks again for your selfless help！
Best wishes
Quxiao
BIT

[Daniele Varsano]

Dear Quixiao,
the definition of the time ordering of Green functions can be found in textbooks. In the retarded case the antiresonant part is also considered. When considering the coupling also the coupling between resonant and antiresonant is taken into account and in this case, the calculation is more cumbersome and usually can be neglected (Tamm Dancoff approximation). As I wrote you in the previous post you can consider the retarded mode to have an accurate real and imaginary part. Of course, you can verify that the Tamm Dancoff approximation applies by considering the coupling terms.

Best,
Daniele

[Quxiao]

Dear Daniele：
Thanks for your help again!
I still have a question. I found that the absolute value of the imaginary part of the dielectric constant for the BSE I calculated with the yambo4.4 system is much smaller than the absolute value of the yambo5.0. Although the trend is the same, the absolute value of this The difference makes me wonder, is there a parameter I haven't noticed that controls this?
This is the result of the same system I calculated with yambo4.4 and 5.0 respectively, except for the absolute value of the imaginary part of the dielectric function, the difference is not big,please give me some help again.
Thanks for your selfness!
Best wishes
Quxiao
BIT

[Daniele Varsano]

Dear Quxiao,
is this a 2D system? In this case the dielectric function is not well defined and the relevant quantity is the polarisability alpha.
When using the cutoff coulomb technique we have modified the response function consistently and this is the reason in the change of absolute value as it is used the truncated potential instead than the 1/q^2 term.

This is explained in the FAQ of the Yambo webpage:
https://www.yambo-code.org/faq/

Note that the website in these days is very slow, we are working to solve the problem.

Best,
Daniele

[Quxiao]

Dear Daniele：
Thanks for your reply!I have learned the link you provided,something I want to sure,
When I use the cutoff coulomb technique, the (polarisability) alpha=-X/q^2,is it?
When I use the yambo -r (cutoff coulomb technique),I could get the polarisability from the o-yambo.out.alpha_q1_diago_bse,is it?
And I also could get the imaginary part of dielectric function from the o-yambo.out.eps_q1_diago_bse ,is it?
I see that formulation:ε = 1 +4πα/d,the alpha(α)=-X/q^2?
The last question is that I have seen that there is a unit of polarizability (length unit) in some literature, so I want to know what is the unit of the polarizability output in yambo?
I am confused,please give me some help
Thanks!
Best wishes
Quxiao

[Daniele Varsano]

Dear Quxiao,

When I use the cutoff coulomb technique, the (polarisability) alpha=-X/q^2,is it?

Yes! but there is a multiplying factor that depends on the dimensionality. For 2D it is multiplied by the non periodic length "d"

And I also could get the imaginary part of dielectric function from the o-yambo.out.eps_q1_diago_bse ,is it?

Yes, it will be proportional to alpha but with very small numbers, going to zero for large volumes.

The last question is that I have seen that there is a unit of polarizability (length unit) in some literature, so I want to know what is the unit of the polarizability output in yambo?

Correct, alpha has the dimension of a length unit and it is in bohr

Best,
Daniele

[Quxiao]

Dear Daniele：
Thanks for your help!
I learn that with your help!
Best wishes!
Quxiao

[Quxiao]

Dear Daniele：
I am a newcomer and have a lot of confusion.I read the yambopy code and successfully realized the exciton projection on the single electron energy band, but now there is a problem. I previously made the orbital projection of the single electron energy band and used the group theory to conclude that there is a transition between the lowest conduction band and the highest valence band. However, the exciton projection I made with yambopy is in the lowest conduction band and the second highest valence band, There is no exciton in the highest valence band, so I doubt the result.

If the projection result is correct, the formation of excitons is higher than the transition selection rule. What's more, I don't understand the physical meaning of the weight of excitons in the energy band projection, because I know that excitons can expand in the electron hole state. Is this weight the expansion coefficient, the expansion coefficient of the electron hole state with specified energy?
Thanks for your help!
Best wishes
Quxiao

[Daniele Varsano]

Dear Quixiao,

the exciton weights are the square modulus of the eigenstate of the BSE which is calculated in transition space.
So,the exciton can be expressed as a linear combination of independent particle transitions:
\Psi_exc=\sum A_cv \psi_v \psi_c
the weights are |A_cv|^2

Note that the energy reported in the weight file, transition energies (Ec_Ev) are the KS energies and not the QP energies.

Best,
Daniele

[Quxiao]

Dear Daniele ：
I understand what you said .However,I still have some questions.Please give me some help.
When I calculate the BSE of anisotropic materials, I can get the absorption spectrum in different directions by setting BlongDir.
Now I have some doubts about this BlongDir parameter. My previous understanding is the propagation direction (momentum
direction) of the incident light, but I am now suspicious, the note here is # [BSS] [cc] Electric Field,
so could this be referring to the direction of vibration of the electric field (shear wave vibration)?
Or is it the direction of propagation of the electric field (same as that of the incident light)?
This is very important to me, looking forward to your reply!
Best wishes！
Quxiao