How to obtain the correct 2D polarizability alpha_2D?

[yhypku]

Dear all,
I want to obtain the two-dimensional polarizability alpha_2D from RPA or BSE calculations. I noticed that there are two ways to do that: 1) calculate it directly from RPA, as in "PHYSICAL REVIEW B 84, 085406 (2011)"; 2) do BSE calculations and get the binding energy, then build a reliable low-energy model and adjust alpha_2D to match the model and first-principle binding energies, as in Nature Nanotechnology volume 15, 367–372 (2020).
I tried these two methods in 2D hBN systems. What confused me is that for a 18*18*1 calculation, the ALPHA-Re(\omega=0) (ALPHA0-Re also) in o-rpa.alpha_q1_inv_rpa_dyson file is different from the one in o-bse.alpha_q1_diago_bse file. Here are my questions:
1) I think the reason for this discrepancy is that I set BSE bands to 2-6, but set BndsRnXd in rpa to 1-60. Is that true?
2) If it's true, does it mean that the correct alpha_2D comes from the RPA output file?
The input and output files are attached.
Best wishes,
Huaiyuan

[Daniele Varsano]

Dear Huaiyuan,

the two calculations differs because you are using two different levels of theory (RPA and BSE).
Parameters are different, but this is not a problem if they are at convergence (this is something you need to check)
Finally, please note that a BSE calculation should be done on top of QP energies and not KS energies so you need to perform either a GW calculation and run BSE on top including the QP energies via the KfnQPdb keyword, or model them by using a scissor operator using the KfnQP_E keyword.

Best,
Daniele

[yhypku]

Dear Daniele,
When all the parameters are converged, results from RPA and BSE are the same. Is that right? I noticed that in o-bse.alpha_q1_diago_bse file, DipBands are the same as BSEBands, to be "2 | 6|". Is that a problem to the result?
Best,
Huaiyuan

[Daniele Varsano]

Dear Huaiyuan,

When all the parameters are converged, results from RPA and BSE are the same. Is that right?

No, they are not, as they contain different physical insight, and RPA misses the electron-hole attraction interaction (excitons).

If you want RPA is the same to the BSE when the x-part only of the kernel is considered, in this case it is just a change of basis set.
Note that in order to obtain the same results, the parameters (bands, and G vectors (in exchange for BSE, Gblk in RPA)) should be the same, moreover you need to pay attention to the time-ordering.

Best,
Daniele