Head term of screened Coulomb interaction in BSE

[clin]

Dear developers,

I am running NEQ_GW calculations in Yambo to obtain the screened Coulomb interaction matrix elements, and found if the head of screened Coulomb potential is included, it leads to the divergence at Gamma point. According to the literature, the head term diverges as 1/q^2 when q-->0 in semiconductors. Since BSE also calculates the same quantity, I wonder how Yambo deals with the divergence of head term of screened Coulomb potential in BSE.

Many thanks,
Changpeng

[Daniele Varsano]

Dear Changpeng,
in BSE the divergence of the potential is removed by integration in a small region around q=0. Depending on if you are using or not, stochastic integration the average is done by Monte Carlo method or by integrating analytically the bare coulomb potential in small sphere.

Best,
Daniele

[clin]

Dear Daniele,

Many thanks for your help.

Yes, I used the RIM integral and I understand this is a technique in Yambo to address the divergence. My doubt is still whether the head term of screened Coulomb potential's contribution should converge to a constant value. By this, I mean when using denser and denser grid, the RIM potential at q=0 will become larger and larger, since the region around q=0 for RIM becomes smaller and smaller. For a super large k/q grid, the RIM W is still diverging because the head term of dielectric matrix is a constant in semiconductor. Or, is it because the head term at q=0 negligible at very dense grid?

Best,
Changpeng

[Daniele Varsano]

Dear Changpeng,

my understanding is that the head term is divergent, but it is integrable, so you can regularize it. For denser and denser grids, its value will increase as 1/q^2, but the integration volume d3q will reduce as q^2. And yes, it will be negligible at very dense grid.

Best,
Daniele