pros and cons of real-time method in nonlinear response calculation

[Jasonyu]

Dear all,

I used sum over states method in IPA to calculate the second-harmonic susceptibility in my research work. However, it is prevented from counting the excitonic effect in the calculation because of increase of the computational cost as mentioned in yambo's real-time method paper[1]. I am very interesting in migrate to using yambo to achieve my purpose. Before I start using the real-time method I have the several questions in my mind:
1) In terms of computational cost, how much of the cost does the real-time method reduce for the same precision?
2) Are there any advantages of sum over states method that real-time method cannot replace?
Looking forward to your reply.

Regards,
Jason

[1] Attaccalite, C., 2016. Non-linear response in extended systems: a real-time approach. arXiv preprint arXiv:1609.09639.

[claudio]

Dear Jason

1) In terms of computational cost, how much of the cost does the real-time method reduce for the same precision?

The computational problem of our real-time approach is that when we want to include excitonic effects,
we need to store a lot of matrix elements of the screened exchange term.
See the appendix of PRB 84, 245110 (https://arxiv.org/pdf/1109.2424.pdf) so we cannot afford too large systems.
You can always resort to some simplified model for excitons, and in this case, it will be possible
to do large systems.

2) Are there any advantages of sum over states method that real-time method cannot replace?

A difficult thing to do with real-time simulations is the analysis of the origin of different peaks in linear and non-linear responses.
It is not impossible but it is complicated and we never worked on it.
Instead, the great advantage is that with the same code you can study different non-linear responses SHG, THG,
two-photon absorption, optical rectification, etc ...
Clearly you have to think of a way to extract these coefficients from your real-time simulation but it can be done.

Try to have a look at the tutorials and see if they fit to your needs:
Tutorials on non-linear response
Linear response from real-time simulations
Real time approach to non-linear response
Correlation effects in the non-linear response
Real time Bethe-Salpeter Equation(TDSE)

In the above tutorials consider only the part related to the real-time Schoeredinger equation (yambo_nl and ypp_nl).
The real-time implementation in terms of density matrix (yambo_rt ypp_rt) cannot be used for the non-linear response.

please add your affiliation to your posts

best
Claudio