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A twin question related to the TDDFT method is asked in another post. But any comparisons between both methods in recent developments are welcome.

The time-dependent density functional theory (TDDFT) and the many-body perturbation theory (GW@BSE) methods are considered as the two most popular and successful methods to describe the excited-stated properties of materials. In fact, both methods have been reviewed in this classical paper published in Review of Morden Physics. From that almost twenty years have passed. What are the recent developments of the GW@BSE method? And what are the current challenges to simulate real materials with the GW@BSE method? As far as I know, the BerkeleyGW GROUP and Yambo GROUP have successfully implemented the framework of the GW@BSE method based on plane-wave DFT calculations. Are there any packages to realize this method, especially without dependence on plane-wave DFT?

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    $\begingroup$ I am not an expert on the question, but there are several different implementations both for plane waves and localized basis. The difference I have found were the different approximations implemented: GW is extremely slow and poorly scaling, so all kind of tricks trying to improve those bottlenecks. Sime codes that include GW, generally several different approximations each (I am not sure BSE): VASP, Turbomole, cp2k $\endgroup$
    – Greg
    Commented Jan 10, 2021 at 9:45

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As one of the members of the Yambo group I can answer for the developments, in the Yambo code, in particular related to GW and BSE. One important aspect is the code optimization, and the connected porting on GPU cards (see the Max Centre of excellence). Work was done in optimizing GW and BSE for 2D materials, see for example the RIM-W method and the multi-plasmon pole approximation; adding support for spin-orbit coupling both in GW and BSE; and computing finite momentum exciton dispersion, which, for example, opens the way to compute exciton-phonon coupling.

The modelling of excitons out of equilibrium is one of the new subjects of interest for the community. Starting from the formulation of the real-time BSE, the recent developments include the study of exciton-phonon coupling in photoluminescence, the signature of excitons in ARPES and transient Absorption spectroscopy.

Going beyond what is in the Yambo code, recent ongoing activity on exciton dynamics both numerical and theoretical. Also very recent theoretical works include the use of MBPT to go from electron-phonon to the modelling of polarons, and ongoing activity to capture exciton-polaron interaction. It is of course not exhaustive, and mostly focused on (part of) my research activity, with also few new recent works that I like on the subject.

Finally a short comment for GW and BSE not in plane wave. There are packages, such as for example the Fiesta code of the MolGW code focused on isolated systems, and for extended systems code such as Elk and Exciting. The list is not at all exhaustive. The GW100 initiative is also a good reference for many other codes.

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