Epsilon_1

[jmmorbec]

Hello.

I am doing BSE calculation using the Inversion method (yambo -o b -b -y i), and I would like to know how Yambo computes the real part of the dielectric constant. Is there any approximation used to compute \eps_1? And are Kramers Kronig relations satisfied?

I really appreciate if someone could help me with this.

[jmmorbec]

Just completing my previous question.
The reason why I would like to understand how BSE calculations with Yambo computes \eps_1 is because my \eps_1(0) obtained using BSE/G0W0 using Yambo is ~21% smaller than that obtained using Density Functional Perturbation Theory with PBE functional and Quantum Espresso.
I know that part of this difference is due to the difference in the band gaps (PBE and G0W0) [Penn model], but I would like to know if this could be related to the Tamm-Dancoff approximation or other approximations using in the BSE calculation of \eps_1 with Yambo.

Thank you!

[Davide Sangalli]

Dear Juliana,
the inversion uses the relation

L= (L_0 - K)^-1 and the fact that eps= < W | L | W >

where L_0 is the "IP" four particles propagator and K is the BSE kernel, both written in configuration space (i.e. K=K_{cvk,c'v'k)}) and W_{cvk}= iq*R_{cvk} with R_{cvk}=<ck|r|vk>.

As for the diagonalization solver you can chose the "resonant" "causal" or "coupling" mode. Thus you can check the effect of the TDA.
Note that "resonant" and "causal" differ only in case you have a metallic system.

In any case the result should be the same of the diagonalization solver or other solvers (but wih the inversion you can use dynamics kernels or the double grid technique). Thus the value of the eps should be meaningful and not arbitrarly defined at least for 3D systems.

Best,
Davide

[jmmorbec]

Thanks, Davide for your reply.
But are the Kramers Kronig relations satisfied?

[Davide Sangalli]

Well they should. But usually yambo does not check.
Just in some cases it uses the KK explicitly. I guess one could check ...

Hope it helps.
Best,
Davide

[luca.montana]

Dear Davide,

(but wih the inversion you can use dynamics kernels or the double grid technique)

Do you mean a dynamic BSE kernel as described in this paper :
"Double excitations in correlated systems: A many-body approach
D. Sangalli, P. Romaniello, G. Onida, and A. Marini"

Bests
Luca

[Davide Sangalli]

In principle yes ... in practice this is not yet in the GPL version.
Maybe in a future release.

Best,
Davide