Notice that the peak is negative if the absorption is constructed from the "retarded" four point propagator.

This is exactly what I observed by going from "resonant" to "retarded" as mentioned before.

The dielectric function contains both absorption and stimulated emission (we usually call it "absorption" just because the emission channel is always zero from the ground state). Then, if light is emitted, the dielectric function must be negative at that energy.

This is very interesting, since I thought that for stimulated emission one needs to calculate contributions from an equation specifically derived for stimulated emission which is not coded in YAMBO.

According to what you say, this makes the negative energies in the positive range fully physical but only if we assume that we have the wrong GS, and consider it as an excited state.

In VASP, I don't see any negative energies in the positive range when including anti-resonant contributions. It is possible that VASP gives incorrect results regarding this issue.

Since one cannot update the wave functions in YAMBO, I will check it with hybrid-DFT as my starting point and look what happens, whether I still get the negative energies or not.

I will let you know.

Best,

Martin