Many-body response functions in the Questaal code

Daresbury Laboratory, UK, 21-25 May 2018

Organizers: Mark van Schilfgaarde, Jerome Jackson, Martin Lueders, and Leon Petit

Splendid sunshine greeted the 29 participants of the second Daresbury Questaal school, which took place between 21 – 25 May 2018.  The focus for the school was the application of the all-electron, full-potential linearized-muffin-tin (LMTO) code Questaal ( to the calculation of response functions with many body perturbation theory and dynamical mean field theory.  The highlight of the school was providing a clear description of these methods alongside practical training in performing such advanced calculations for real material problems and experiments.  The school was sponsored by the CECAM Daresbury node, the UK’s CCP9 collaboration and the Psi-k network.

The aim of the school was to enable the participants to derive optical and magnetic responses of materials by training them in the relevant theories an instructing them in the operation of the different codes in the Questaal package.  The need for advanced theories for calculating response functions was made clear in a talk by Toby Perring (ISIS Neutron and Muon Source) who gave a detailed introduction into the capabilities and relative merits of modern neutron and x-ray scattering techniques.

The practical part of the school started with an introduction to the full-potential density functional code at the heart of the package which serves as the starting point for applying the more advanced methods presented later.  Participants were shown how to get step by step from simple crystal information, such as a “.cif” file, to relaxing internal coordinates, plotting band structures and calculating the RPA dielectric function.  Detailed lectures by Mark van Schilfgaarde (King’s College London) the main developer were accompanied by guided “hands-on” instruction by Jerome Jackson (CCP9 and Daresbury Laboratory).

In the second part of the school, the students were introduced to qsGW theory and its implementation in the Questaal package; especially about the nature of the quasiparticle selfconsistency.  This represents a significant improvement over density functional theory that is truly ab-initio and parameter-free.  Further hands-on sessions guided the students in how to setup and run such calculations and how to analyse the results.  The GW approach was extended by the new implementation of ladder diagrams to the screening, W, via the Bethe-Salpeter equation.  This approach is the correct formalism for describing excitonic effects in materials and, for materials where the exciton binding energy contributes significantly to the fundamental gap, such as LiF or NiO this method significantly improves upon, among other things, the usual qsGW bandgaps, giving very close agreement with experiment.  The BSE theory was presented by Myrta Grüning (Queen’s University Belfast) and how to use it in Questaal was presented by Brian Cunningham (Queen’s), who recently implemented the method in the code.

The final days of the school were dedicated to dynamical mean-field theory.  After a presentation of the conceptual basis and motivation for DMFT by Silke Biermann (Ecole Polytechnique), practical demonstrations were given by Swagata Acharya (King’s College London).  Unlike many implementations, the Questaal approach allows the combination of DMFT, which gives a numerically exact treatment of local correlations with qsGW, which gives a much better description of the dispersive bath states than that of DFT.  This combination qsGW+DMFT represents the state of the art for materials modelling and the participants were able to perform such calculations, taking NiO and FeSe as prototypical examples where the incorporation of DMFT is significant.   The participants were also guided through the process of extracting spectra (analytic continuation via Pade approximation or maximum entropy methods) from the Matsubara-axis data provided by the continuous-time quantum Monte Carlo solver used for the  impurity problem.

Feedback from the participants, who were almost exclusively at post-doctoral level, was very positive and confirms the value of combining advanced lectures with practical guided hands-on tuition.  By giving participants the opportunity to try the different methods themselves, and to obtain immediate help and guidance, significantly simplifies the process of learning these complicated methods. Lecture materials have been made available to the participants via the CCP9 website:


21 May

Welcome and Introduction to the LMTO Method  Mark van Schilfgaarde (King’s)
DFT Tutorial and Hands-on   Jerome Jackson (DL)

22 May

Introdution to Correlated Systems   Mark van Schilfgaarde
Spectroscopy with Neutron and X-ray Synchrotrons   Toby Perring (ISIS)
GW Tutorial and Hands-on   Mark van Schilfgaarde

23 May

Many-body Perturbation Theory   Myrta Grüning (QUB)
Bethe-Salpeter Tutorial and Hands-on   Brian Cunningham (QUB)

24 May

Dynamical Mean Field Theory   Silke Biermann (E.Polytechnique)
DMFT Tutorial and Hands-on   Swagata Acharya (King’s)
Social Dinner

25 May

Response Functions in DMFT   Swagata Acharya
Response Functions in DMFT Tuturial   Swagata Acharya

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