WARNING : Not Linear values of Sigma_c

[lorenzo.sponza]

Hallo to everybody.
I have some wired results on computing spectral functions: the Imaginary part of sigma behaves as I expected (like eps^{-1}), but the real part of Sigma is "too high".
It has the good shape but is somewhat shifted on the y axis.

Looking at the log I fond this warning:

m_dyson_solver.F90:234:WARNING
Values of Re Sig_c are not linear
band index = 8 spin|component = 1
root mean square= 0.011770049967972
estimated slope = -0.901219504469804
Omega [eV] SigC [eV]
17.5200-17.2939
17.7700-17.6882
18.0200-17.3734
18.2700-17.6088
18.5200-17.8956
18.7700-18.6415
19.0200-18.7743
19.2700-18.1610
19.5200-19.3602

Can this be related with my problem?
What does this warning mean?

Thanks a lot.

[gabriel.antonius]

It seems there is a problem computing the renormalization factor "Z".
As you probably know, the equation
E = E0 + Sig(E) - Vxc
is approximated by
E = E0 + Z ( Sig(E0) - Vxc)
with the renormalization factor is
Z = (1 - d Sig_C (omega) / d omega )^-1
evaluated at omega = E0.

This is assuming that E and E0 are relatively close, and that Sig_C is a smooth function near E0. Now, the code finds that Sig_C is not very linear, because it can hardly fit a linear curve from the values computed at 9 frequencies near the original energy, which makes the approximated solution shaky.

While it is not impossible that this non-linearity of Sigma is intrinsic to your system, it might also be a numerical artifact resulting from coarse parameters. I would suggest to:
- Increase the number of frequencies computed on the real axis (nfreqre), as I assume you are making a contour-deformation calculation.
- Increase the number of k-points.

Let me know if it works.

[Chem]

I Have the same problem but in the case of Plasmon Pole calculations; I get the following Warning :

m_dyson_solver.F90:233:WARNING
Values of Re Sig_c are not linear
band index = 1 spin|component = 1
root mean square= 0.125980718165803
estimated slope = 3.421683573924189
Omega [eV] SigC [eV]
-36.4580 24.8972
-36.2080 22.4751
-35.9580 16.2393
-35.7080 30.5499
-35.4580 24.0975
-35.2080 26.0632
-34.9580 29.0470
-34.7080 27.8833
-34.4580 28.3902

[lorenzo.sponza]

It seems there is a problem computing the renormalization factor "Z".
While it is not impossible that this non-linearity of Sigma is intrinsic to your system, it might also be a numerical artifact resulting from coarse parameters. I would suggest to:
- Increase the number of frequencies computed on the real axis (nfreqre), as I assume you are making a contour-deformation calculation.

Indeed I am doing a contour-deformation calculation. Do you really mean I have to change nfreqre (parameter of the SCR file) or you mean nfreqsp?
I imagine that the number of frequencies to increase is that where Sigma is computed, not the SCR file. So it hould be nfreqsp.
Am I right?

- Increase the number of k-points.

Can I do that without computing the SCR again? I guess no, right?

Thanks for your help.

[gabriel.antonius]

I really mean changing nfreqre, not nfreqsp, and changing the number of k-points requires doing the SCR again.

The reason I suggest this, is that the expression for Sigma(omega) looks like this:

\Sigma_{k, i} (\omega) = \sum_{q, n} \int d \omega' M(q, \omega') / ( \omega' - \omega + E_{k+q, n} - i \eta )

Where M(q,\omega) involves the screening and oscillator matrix elements.

The point here is that the denominator is a difference of omega with omega' and E_{k+q, n}. The variable nfreqre determines the number of frequencies omega' for the integration on the real axis, and the number of k-points will be the number of q-points that are summed. Hence, increasing both the number of k-points and real frequencies should make Sigma smoother.