Yambo Community Forum

Dear Sir,
While doing Electron-Phonon calculation in Yambo-py we go for random q-point generation unlike the phonon calculation done in yambo where we do sampling using Monkhorst-Pack mesh. I want to understand that why we need to take random q-points? Is it possible to do electron-phonon calculation with Monkhorst-Pack grid sampling??

Regards,
Himani Mishra

Dear Himani,

Both methods are ok to sample the Brillouin zone and you can choose the one that you think its better.
The calculations of the electron self-energy due to electron-phonon interaction require a good sampling of the Brillouin zone and careful convergence checks.
Using random q-grids has the advantage that you can increase the number of q-points included in your calculation by just calculating more q-points and giving them a new weight in the integral as 1/Nq (Nq is the number of q-points).
Also in random grids, you can give more importance to regions on the Brillouin zone that have a larger contribution to the integrals (this requires some kind of adaptative sampling).
With regular meshes normally you increase the number of k and q points until you are converged. This has a drawback that if you are not converged with for example 12x12x12 you will have to do for example a 16x16x16 which means you will be calculating repeated points.

The general consensus in the literature is to use random q-grids for the self-energy:
https://journals.aps.org/prl/abstract/1 ... 107.255501
https://journals.aps.org/prl/abstract/1 ... 105.265501
https://journals.aps.org/prb/abstract/1 ... .93.155435
https://www.sciencedirect.com/science/a ... via%3Dihub

Now for the convergence of the two cases, you can find some useful discussions here:
In the case of a random Q-grid the error should go as 1/sqrt(Nq)
(see https://en.wikipedia.org/wiki/Monte_Carlo_integration)
In the case of regular grids, the error should decrease as 1/[Nq^(2/d)] where d is the number of dimensions
(see https://math.stackexchange.com/question ... -integrals)
This would seem to indicate that regular grids are better for integrals in less than 4 dimensions.

But don't take my word for it.
If you reach some conclusion about this topic please share.

Cheers,
Henrique

miranda.henrique wrote: Using random q-grids has the advantage that you can increase the number of q-points included in your calculation by just calculating more q-points and giving them a new weight in the integral as 1/Nq (Nq is the number of q-points).
Henrique

Dear Henrique,
How do we understand this? Do you mean for the increased q-points, we can add some new points just behind the previous ones and give a another weight?
Let's take a example: in my calculation I used 80 random q-points and all the weights are 1.0, then I can add anther q-points after this list of q , like
another 30 points after the 80 ones, and give the weights as 1/110? If so, the ph. x calculation should use 'recover=true?

Thanks!

Shudong