Self-consistent GW on eigenvalues only

In this tutorial you will learn how to perform self-consistent GW on eigenvalues only for G or both G and W (evGW). For molecules systems and also for many solids, the G₀W₀ approach often gives poor results. The main reason of this failure is that the DFT starting point with local or semi-local exchange correlation functionals give a too small gap compared with the experimental one, and a single shot GW is not able to correct this error. In order to overcome this problem a possible solution is to use as starting point a hybrid functional like PBE0, B3LYP,HSE etc.. or to perform a self-consistent GW. In general in self-consistent GW also the wave-function should be updated, but for many systems DFT wave-functions are already quite good and a self-consistency on eigenvalues only can be sufficient, for a discussion see for example ref.

In this tutorial we will show how to perform self-consistent GW on the eigenvalues only with the Yambo code.

1. Generate an input file for a G₀W₀ calculation as explained in the GW basics tutorial doing:
   yambo -X p -g n -p p -V qp -F yambo_g0w0_input.in
2. run your first GW calculation doing:
   yambo –F yambo_g0w0_input.in -J G0W0
3. at the end of the run you will get a quasi-particle file o-G0W0.qp.
   Now you can read this new quasi-particle band structure and perform another GW.
   
4. copy your gw input in a new file: cp yambo_g0w0_input.in yambo_g1w1_input.in
5. modify the yambo_g1w1_input.in to force Yambo to read the previous quasi-particle corrections
   GfnQPdb= "E < ./G0W0/ndb.QP"
   and
   XfnQPdb= "E < ./G0W0/ndb.QP"
   
6. repeat point 1) and 2) for the G1W1, G2W2, etc… until the differences between o-GnWn.qp and o-Gn+1Wn+1.qp are small enough.

Usually self-consistent GW converges in about 3/4 iterations. Notice that self-consistency on the eigenvalues can modify the energy level orders. Moreover evGW removes large part of dependency of the GW results from the DFT functional.

If you want to perform self-consistency only on G and not on W comment the line: #XfnQPdb= "E < ./GW0/ndb.QP"

Convergence issues: convergence parameters for the self-consisntet GW are the same of the standard GoWo calculation plus the bands range employed for the self-consistency, that has to be careful checked.

Internal and external self-consistency in Yambo: In Yamo there is another way to perform self-consisent GW, t

As example you can consider the results on hexgonal-Boron Nitride in ref.