Yambo Community Forum

Dear Daniele,

The dynamically screened interaction W is given as the integral over the inverse of the dielectric matrix eps_G,G'(q, omega) multiplied by the bare interaction v.

my question is whether W is calculated by YAMBO over a frequency integral for the FULL eps_G,G'(q, omega) matrix OR
is it calculated over a frequency integral for the G=0, G'=0 components of the inversed eps_G,G'(q, omega) matrix?


Best,
Martin

Dear Martin it is computed over a frequency integral for the FULL eps_G,G'(q, omega) matrix.
In src/pol_function/X_irredux.F
yambo computes the full Xo_G,G'(q,omega).
The latter is then used to get X_G,G'(q,omega) solving the dyson equation for X and finally eps^-1_G,G'(q,w)
eps_M(q,omega) (the macroscopic term) is defined as the inverse of the head when doing "yambo -o c" calculations.

Otherwise the full eps^-1_G,G'(q,w) is used to construct the GW self-energy for example.
Notice that if the PPA is used, eps^-1_G,G' is computed for two frequencies only, 0 and omega_p, and then interpolated for the other frequencies.

Best,
D.

Dear Davide,

many thanks for your reply.

That means, that the GW self-energy is constructed in YAMBO as a summation of head and wings of W_G,G'(q,omega), right?

eps_M(q,omega) (the macroscopic term) is defined as the inverse of the head when doing "yambo -o c" calculations.

This is a point I always asked myself. Are the other diagonal and OFF-diagonal elements of
the inverse of the microscopic dielectric matrix really so unimportant for the optical absorption spectra?

I have another question regarding calculation of optical spectra with respect to finite q.
Is it still not possible to run finite q BSE calculations? If I remember correctly, this was implemented by Claudio Attaccalite in his own version of YAMBO, however I can not find it any more on GitHub.

Best wishes,
Martin

Dear Martin,
in GW the self energy is built using the whole eps^-1_GG' matrix:
Wgg'(q,w)=eps^-1gg'(q,w)v(q+g')

In absorption, as said by Davide, the macroscopic dielectric function is defined as the head of the inverse of eps_gg'
eps_M(w)=1/(eps^-1)_00 which is different from eps_00 (non-interacting case).
In order to invert the eps matrix, you need all the non-diagonal terms: these are what are called the local field effects.

Finite q BSE it is actually in the devel version of the code, we are still testing it, therefore it is not available in the gpl version,
and at this moment I cannot tell you when it will be released.

Best,

Daniele

Dear Daniele,

in GW the self energy is built using the whole eps^-1_GG' matrix:
Wgg'(q,w)=eps^-1gg'(q,w)v(q+g')

The point is that the integral over frequency is over components of Wgg'(q,w) (spitted into head and wings) because there is a summation over G and G' before the frequency integral (as you can see in the picture).
Is this the way how YAMBO calculates the GW self-energy?

I struggle to accurately understand how the off-diagonal elements of W are treated for the self-energy.
Again by splitting W into head and wings components OR by directly performing a frequency integral over the full Wgg'(q,w) matrix for each component of W?


According to my understanding : the GW self-energy is given as a sum of frequency integralS over G,G' components of W.

Thanks and best wishes
Martin

Dear Martin,
when plasmon pole is used the integral is performed analytically.
Otherwise it in real axis integration yambo calculate the full matrix eps^-1gg'(q,w) for each frequency (the number of frequencies is given in input), and then the expression you reported is evaluated by performing the sum_gg' and bands for each frequency and then the integral is evaluated exploiting Kramers Kronig relations. If you are interested you may have a look at the following subroutines:
/src/qp/QP_real_axis.F
/src/qp/QP_W2Sc.F

Best,
Daniele