Question regarding divergence treatment in BSE

[doronwu]

Dear developers,

I recently read the 2019 PRL paper about the BSE: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.237402. In the SI, Eq. (18) mentions that the divergence in Eq. (17) is handled using the “g-b” method combined with Monte Carlo integration

From my understanding, this divergence is related to the screened exchange term, and I was expecting to find the corresponding implementation in calc_tau.f90. However, it appears that the actual treatment of the divergence is performed in the subroutine west_apply_liouvillian, and it seems to be implemented simply as a shift like scissor ope.

I might be misunderstanding the structure, so I would appreciate it if you could clarify whether the divergence treatment described in the paper is indeed implemented in west_apply_liouvillian, and how this relates (if at all) to calc_tau.f90.

Thank you very much for your time.

Best regards,
Doron Wu

[vyu16]

Please have a look at the bse_start subroutine in file Wbse/wbse_setup.f90.

Note that in the 6.2.0 release of WEST, the divergence term is wrong when using the HSE hybrid functional. A fix will be released shortly.

[doronwu]

Please have a look at the bse_start subroutine in file Wbse/wbse_setup.f90.

Note that in the 6.2.0 release of WEST, the divergence term is wrong when using the HSE hybrid functional. A fix will be released shortly.

Yes I have checked the div are defined in SUBROUTINE wbse_setup().

When doing Wbse/wbse_davidson_diago.f90, it will call
SUBROUTINE west_apply_liouvillian from td_liouville_oper

Then from line 237 as shown below, sigma_x_head and sigma_c_head are used, but why these terms are not in the screened exchange integral (wbse_init) instead these terms are directly added to the liouville operator like scissors when we do BSE.

Also, from the paper I mentioned, I would expect in the wbse_init calculation, the W would have "g-b" and "default" for vc and vc(chi+f_xc)vc, respectively. However, I only saw "default" are used in SUBROUTINE wbse_init_setup.

     ! Subtract the eigenvalues
     !
     IF(l_bse) THEN
        factor = -scissor_ope+sigma_x_head+sigma_c_head
     ELSEIF(l_hybrid_tddft) THEN
        factor = -scissor_ope+sigma_x_head*exxalfa
     ELSE
        factor = -scissor_ope
     ENDIF

Could you clarify why these terms are not applied directly in the wbse_init calculation and instead added like scissor opt.

Bests,
Doron Wu