Degeneracy of the Top Valence Bands in GW for Si with SOC

Hi everyone,
I performed GW calculations for Si using the same input parameters as in the reference dataset NOMAD, but with spin-orbit coupling (SOC) included.

As expected, the top valence band should not be degenerate for Si with SOC. However, I observed that the degeneracy is lifted only up to 10⁻³ eV.

To improve convergence, I reduced epsengy and epschg to 10⁻⁸, but the GW energies did not change significantly. Given this, I am wondering if there are further refinements that could improve the precision of these energy differences within the GW framework.

Would adjusting other convergence parameters (e.g., k-point grid density, number of empty states, or self-energy corrections) help in resolving this issue? Has anyone encountered a similar effect in GW calculations with SOC?

Looking forward to insights from the community!
Best regards,
sareh