Understanding Differences in RPA (IP) Approaches for Optical Properties in Quantum ESPRESSO and Yambo

[Ehsanulazim]

Hello Dear yambo experts,

I have a question regarding the Independent Particle Random Phase Approximation (IP RPA) for optical properties calculations, specifically comparing Quantum ESPRESSO and Yambo.

In Quantum ESPRESSO, I typically use epsilon.x to calculate optical properties like the dielectric function, and as I understand, this calculation is done at the IP RPA level.

From what I’ve read about Yambo, it also supports optical properties calculations at the RPA (IP) level, but additionally includes more advanced methods like GW and the Bethe-Salpeter Equation (BSE). My understanding is that GW accounts for quasiparticle energies and helps address the band gap problem, while BSE provides a more sophisticated treatment of excitonic effects, though it is computationally demanding.

However, I'm curious about how the RPA (IP) method in Yambo differs from the one in Quantum ESPRESSO. If I run a calculation with Yambo at the RPA (IP) level, will I obtain the same results as with epsilon.x in Quantum ESPRESSO? My understanding is that, at the RPA (IP) level, Yambo also excludes electron-hole interactions and is based on single-particle excitations, similar to epsilon.x. Are there any subtle or fundamental theoretical differences between the two?

I’d appreciate any insights or clarifications on this!

Thank you!

Kind Regards
Ehsanul Azim
Masters Student
Mechanical Engineering
University of Texas Rio Grande Valley

[Daniele Varsano]

Dera Ehsanul Azim,

there is a bit of confusion in the term RPA in the literature.
RPA is often used to indicate IP response function (X^0), but in some papers/reviews/book it is also used to indicate the response function when local field effects are included e.g. the response function X solution of the Dyson equation: X=X^0+X^0vX

The "IP" spectra calculated by Yambo and epsilon.x should be the same, unless there could be different approximations in the calculation of the dipoles. I'm not sure that epsilon.x takes into account the commutator of the non-local part of the pseudopotential (see eq.2) in the Yambo cheatsheet: https://wiki.yambo-code.eu/wiki/images/ ... et-5.0.pdf

In that file, you can find most of the expressions of the quantity implemented in Yambo.

Best,

Daniele