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Discussion Meeting on Electron Correlation

published by francesco on Mon, 04/11/2022 - 12:21

April 27-28, 2022

The gdr REST organizes this discussion meeting on Electron Correlation, both from condensed matter physics and quantum chemistry points of view.

This is not a conference with a series of talks. Please keep in mind the following points: 1) we would like to remind to the informal character of the meeting. The idea is to come with ideas and open issues. Questions are as welcome as (if not more welcome than) the answers. 2) prepare a set of slides to launch discussions on your topic (imagine an undisturbed talk of 20 minutes).
You will be interrupted continuously so it's not impossible that you do not finish everything you wanted to say. This is not a problem! It means that the first slides were already very interesting and we wanted to dwelve on them. 3) other people can pitch in during your talk, with a related topic, similar issue, different approach. Please accept that, for it will make the discussion much more lively. Just to give you an idea, it already happened that a speaker didn't go beyond his second slide: it just started a lively discussion that went on for almost an hour, at which point we stopped.

The workshop takes place in Palaiseau, at the École Polytechnique.

Organisers: Francesco Sottile, Lucia Reining, Matteo Gatti, Pina Romaniello

Speakers:

  • Pierre-Francois Loos (Toulouse, France)
  • Emmanuel Fromager (Strasbourg, France)
  • Stefan Rost and Christoph Friedrich (Jülich, Germany)
  • Julien Toulouse (Paris, France)
  • Maria Hellgren and Thomas Pitts (Paris, France)
  • Andrea Marini (Rome, Italy)
  • Robinson Outerovitch (Bruyères-le-Châtel, France)

Program 1


09:30

Self-consistent density-functional theory without density functionals: A quantum embedding perspective

9:30 - 10:30
Emmanuel Fromager

Unphysical Discontinuities, Intruder States and Regularization in GW Methods

09:30 - 10:30
Pierre-Francois Loos

10:30

Take a break

11:00

Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model

11:00 - 12:00
Julien Toulouse

Is the "exciton" a real particle or just the result of the experimental measure?

11:00 - 12:00
Andrea Marini

12:00

Lunch break

14:00

EELS in 2D systems

14:00 - 15:00
Stefan Rost and Christoph Friedrich

localized electronic correlations in DFT and beyond for solids

14:00 - 15:00
Robinson Outerovitch

15:00

Take a break

15:30

Hydrogen chain with RPA/RPAx

15:30 - 16:30
Maria Hellgren and Thomas Pitts

Title

Maria Hellgren (Paris, France)

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Self-consistent density-functional theory without density functionals: A quantum embedding perspective

Emmanuel Fromager (Strasbourg, France)

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Quantum embedding is a divide and conquer strategy that aims at solving the electronic Schrödinger equation of sizeable molecules or extended systems. In this talk, I will present an in-principle-exact connection between density matrix embedding theory (DMET) [1] and density-functional theory (DFT) within the simple but nontrivial one-dimensional Hubbard model [2]. For that purpose, I will use a recent reformulation of single-impurity DMET as a Householder transformed density-matrix functional embedding theory (Ht-DMFET) [3]. On the basis of well-identified density-functional approximations, a self-consistent local potential functional embedding theory (LPFET) will be formulated and implemented. Combining both LPFET and DMET numerical results with our formally exact density-functional embedding theory reveals that a single statically embedded impurity can in principle describe the density-driven Mott–Hubbard transition, provided that a complementary density-functional correlation potential (which is neglected in both DMET and LPFET) exhibits a derivative discontinuity (DD) at half filling [2].

[1] G. Knizia and G. K.-L. Chan, Phys. Rev. Lett. 109, 186404 (2012). 
[2] S. Sekaran, M. Saubanère, and E. Fromager, Computation 2022, 10, 45.
[3] S. Sekaran, M. Tsuchiizu, M. Saubanère, and E. Fromager, Phys. Rev. B 104, 035121 (2021).

Basis-set correction based on density-functional theory: Rigorous framework for a one-dimensional model

Julien Toulouse (Paris, France)

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We reexamine the recently introduced basis-set correction theory based on density-functional theory consisting in correcting the basis-set incompleteness error of wave-function methods using a density functional. We use a one-dimensional model Hamiltonian with delta-potential interactions which has the advantage of making easier to perform a more systematic analysis than for three-dimensional Coulombic systems while keeping the essence of the slow basis convergence problem of wave-function methods. We provide some mathematical details about the theory and propose a new variant of basis-set correction which has the advantage of being suited to the development of an adapted local-density approximation. We show indeed how to develop a local-density approximation for the basis-set correction functional which is automatically adapted to the basis set employed, without resorting to range-separated density-functional theory as in previous works, but using instead a finite uniform electron gas whose electron-electron interaction is projected on the basis set. The work puts the basis-set correction theory on firmer grounds and provides an interesting strategy for the improvement of this approach.

Unphysical Discontinuities, Intruder States and Regularization in GW Methods

Pierre-Francois Loos (Toulouse, France)

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By recasting the non-linear frequency-dependent GW quasiparticle equation into a linear eigenvalue problem, we discuss the appearance of multiple solutions and unphysical discontinuities in various physical quantities computed within the GW approximation. Considering the GW self-energy as an effective Hamiltonian, we will show that these issues are key signatures of strong correlation in the (N ± 1)-electron states and can be directly related to the intruder state problem. A simple and efficient regularization procedure inspired by the similarity renormalization group will be proposed to avoid such issues and speed up convergence of partially self-consistent GW calculations.

E. Monino & P. F. Loos, arXiv:2202.11589 [physics.chem-ph]

Title

Author (City, France)

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Is the "exciton" a real particle or just the result of the experimental measure?

Andrea Marini (Roma, Italy)

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Anna Galler (Hambourg, Germany)

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EELS in 2D systems

Stefan Rost (Jülich, Germany)

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List of Participants

  1. Abdallah El Sahili
  2. Alam Osorio
  3. Andrea Marini
  4. Christine Giorgetti
  5. Christoph Friedrich
  6. Diata Traore
  7. Emma Nogue
  8. Emmanuel Fromager
  9. Francesco Sottile
  10. Gabriele Riva
  11. Georg Michelitsch
  12. Jörn Stöhler
  13. Julien Toulouse
  14. Laura Urquiza
  15. Lionel Lacombe
  16. Lucia Reining
  17. Maria Hellgren
  18. Matteo Gatti
  19. Pierre-Francois Loos
  20. Pina Romaniello
  21. Rajarshi Sinha Roy
  22. Robinson Outerovitch
  23. Stefan Rost
  24. Timothée Audinet
  25. Tom Pitts
  26. Valérie Véniard
  27. Valerio Olevano
  28. Vitaly Gorelov

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