full BSE calculation

[Jing Liu]

Dear developers,
My issue is in running a full BSE calculation with BSEmod = "coupling" and WehCpl.
Comparing with my previous BSE calculation (TDA) with BSEmod = "retarded", I got the almost totally the same spectrum.
But the file "o-BSE.exc_E_sorted" in these two calculations are totally different.
In the tutorials I find the notice as "you will find many exciton with negative energy due the full-BSE nature".
So how should I understand the results of the full BSE calculation? What's the different between the files "o-BSE.exc_E_sorted" in these two calculations?

Thanks so much!

Best,
Jing Liu

[Daniele Varsano]

Dear Jing,

if the spectrum are very similar it means that the coupling is not needed.
When you add the coupling you have both resonant and anti resonant excitations, if the coupling has not effect they are very similar.
In both o-BSE.exc_E_sorted the excitations are sorted in ascended order, so in the full calculation you have the negative energy excitations (c-->v) first.

Best,
Daniele

[Jing Liu]

Dear Daniele,
Thanks for your quick reply.
If I want to verify the Excitonic Insulator state, the lowest exciton would have a negative energy. I can judge it directly through the file "o-BSE.exc_E_sorted" in the TDA calculation.
But If I use full BSE calculation, the lowest excitonic energy is so large (-6.726 eV). (In TDA, it is -0.271 eV).
I am confused that do they represent the same physics for the first column of the file "o-BSE.exc_E_sorted" in the two different calculations?

Thanks again!
Best,
Jing Liu

[Daniele Varsano]

Dear Jing,

if course in a full calculation you have large negative excitations but these are due to c-->v transitions (you can verify it analysing the excitation weight) so they have a very different meaning.

To be clear, the BSE provides you both resonant and anti resonant excitations, ie v-->c and c-->v, in a TD calculation the anti-resonant are not reported as they are assumed to be
Eantires=-Eres

Best,
Daniele

[Jing Liu]

Dear Daniele,
Thanks so much for your kind reply!

Best,
Jing Liu

[Jing Liu]

Dear Daniele,
I have another question that what's the meaning of the fourth column named "W [meV]" in the "o-BSE.exc_E_sorted". Does it means the eh interaction?

o-BSE.exc_E_sorted.jpg

Thanks a lot!

Best,
Jing Liu

[Daniele Varsano]

Dear Jing,

it is the widths of the excitations (related to the lifetime). It appears as in the full BSE you can have complex eigenvalues, so essentially it is the imaginary part of the eigenvalue.
As electron-phonon interaction is not included they are typically very small and you can ignore.

Daniele

[Jing Liu]

Dear Daniele,

Thanks so much! I got it!

Best,
Jing Liu

[Jing Liu]

Dear Daniele,
I do the full BSE test in another system by using the BSEmod = "coupling" and uncomment the WehCpl. But I can not obtain the column named "W [meV]" in the "o-BSE.exc_E_sorted" file as before.
So I want to know which tag in the input file control this "W [meV]" output and where can I find the mathematical expression of the "W".
And, how can I judge the excitonic insulator state (to see whether the lowest exciton energy is negative) in full BSE calculation?

Thanks a lot!

Best,
Jing

[Daniele Varsano]

Dear Jing,
The width W is reported only when the imaginary part of the eigemvalue is larger than a default threshold (10^-5, if I'm not wrong). This info I would say is rather irrelevant.

If you want to look at exciton instabilities, in presence of coupling terms, you need to look at negative eigenvalues having v-->c components in their eigenvectors.

Best,
Daniele