Non density-density Coulomb terms in the calculation of GW_sigma

[the-hampel]

Summary

This problem is only present in the current unstable version of TPRF.

The current functions gw_sigma and g0w_sigma only consider density-density type interactions in the calculation of Sigma and neglect all other terms. It would be good if the user would be either be warned if some matrix elements of the interaction are neglected or if those are all considered.

I believe the function gw_sigma neglects those terms in the static components, but correctly considers them in the dynamic part, whereas the real frequency version using the spectral representation g0w_sigma neglects them completely.

possible solution

1. Warn the user if his Coulomb interaction contains non density-density type terms and those would be neglected.
2. Add the possibility to also consider non den-den terms in both functions. Most importantly in the Matsubara version.
3. If this is performance critical we can add a switch to sum over those elements or neglect them?

Let me know what you think.

• Alex