Real-axis GW

[vormar]

Dear Developers,

I am about to try the real-axis GW option that is now available in the GPL release. I am not yet certain how this is actually done and which
parameters affect the calculation besides usual parameters (FFTGvecs, GbndRnge, BndsRnXd, NGsBlkXd, etc.). Therefore I have some basic questions...

First, is there any theoretical paper or slide that tells how this is done actually? In my opinion this is not straightforward at all and there are many different ways of calculating the full frequency dependent screening.

Using the tutorial on LiF I found that the dynamical dielectric matrix is evaluated at 100 frequencies from 6.2868 to 80.77806 eV. So, here comes my second question: how is the frequency interval chosen? If I'm right then in this case all possible dft single particle excitations lie in this energy range.

I suppose that 100 comes from ETStpsXd and the resulting discrete function is smoothed with a lorentzian function specified by DmRngeXd. In principle, ETStpsXd should be a convergence parameter: the denser the grid, the better the result. However I think this is not true for DmRngeXd. Am I right about this?

Thanks in advance,
Marton

[myrta gruning]

Hallo Marton

First, is there any theoretical paper or slide that tells how this is done actually? In my opinion this is not straightforward at all and there are many different ways of calculating the full frequency dependent screening.

You can find details in Andrea Marini's thesis

Using the tutorial on LiF I found that the dynamical dielectric matrix is evaluated at 100 frequencies from 6.2868 to 80.77806 eV. So, here comes my second question: how is the frequency interval chosen? If I'm right then in this case all possible dft single particle excitations lie in this energy range.

Yes you are right.

I suppose that 100 comes from ETStpsXd and the resulting discrete function is smoothed with a lorentzian function specified by DmRngeXd. In principle, ETStpsXd should be a convergence parameter: the denser the grid, the better the result. However I think this is not true for DmRngeXd. Am I right about this?

Yes again. Ideally ETStpXd should be infinite and DmRngeXd should be 0.

Regards,
Myrta

[vormar]

Hi Myrta,

Hallo Marton

First, is there any theoretical paper or slide that tells how this is done actually? In my opinion this is not straightforward at all and there are many different ways of calculating the full frequency dependent screening.

You can find details in Andrea Marini's thesis

Thanks!

Using the tutorial on LiF I found that the dynamical dielectric matrix is evaluated at 100 frequencies from 6.2868 to 80.77806 eV. So, here comes my second question: how is the frequency interval chosen? If I'm right then in this case all possible dft single particle excitations lie in this energy range.

Yes you are right.

OK. Then maybe it is a naive question, but why isn't the static limit included in this range? The plasmon-pole approximation is based on the knowledge of the system in the static limit and in some cases in an imaginary frequency (Godby-Needs model). Why don't we need this information in the real-axis calculation?

I suppose that 100 comes from ETStpsXd and the resulting discrete function is smoothed with a lorentzian function specified by DmRngeXd. In principle, ETStpsXd should be a convergence parameter: the denser the grid, the better the result. However I think this is not true for DmRngeXd. Am I right about this?

Yes again. Ideally ETStpXd should be infinite and DmRngeXd should be 0.

Regards,
Myrta

Is there any rule of thumb that estimates how many frequency points are needed? I would say that it is meaningless to get the frequency spacing much denser than the single particle energy spacing so the frequency density around 10/eV should be considered to be converged in many cases. Is this true?

I know that convergence always depends on the specific system, but do you have any experience on convergence trends? I already found nearly convergent parameters for my system with pp-GW if I'm interested in the gap correction. However I'm not sure that the same parameters yield the same accuracy if I switch on real-axis GW and leave other parameters untouched.

Thanks,
Marton

[andrea marini]

OK. Then maybe it is a naive question, but why isn't the static limit included in this range? The plasmon-pole approximation is based on the knowledge of the system in the static limit and in some cases in an imaginary frequency (Godby-Needs model). Why don't we need this information in the real-axis calculation?

In the PPA you choose two frequencies to FIT the inverse dielectric function on the imaginary axis. In the real-axis calculation you need to perform a numerical Kramers-Kronig trasformation of the screened interaction. As it is explained in my thesis this is done by defining the spectral function of the inverse dielectric function. This function is, by definition, zero within the gap. Therefore the zero frequency is not included in the range. Of course after the Kramers-Kronig trasformation also the static limit is correctly included.

Is there any rule of thumb that estimates how many frequency points are needed? I would say that it is meaningless to get the frequency spacing much denser than the single particle energy spacing so the frequency density around 10/eV should be considered to be converged in many cases. Is this true?

I would say that you need to use a frequency step smaller or equal to the step needed to calculate the self-energy derivative. Normally 0.1/0.2 eV shoud be enough.

I know that convergence always depends on the specific system, but do you have any experience on convergence trends? I already found nearly convergent parameters for my system with pp-GW if I'm interested in the gap correction. However I'm not sure that the same parameters yield the same accuracy if I switch on real-axis GW and leave other parameters untouched

Actually, except for the number of frequencies all other parameters can be imported from a converged PPA calculation. But I suggest you to perform same small test to see if you are really near convergence.

Andrea