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Pierre-Francois Loos committed Jan 31, 2024
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### Cyril Martins (LCPQ, Toulouse)

**An introduction to Dynamical Mean-Field Theory**
<a href="/presentations/CMartins.pdf">An introduction to Dynamical Mean-Field Theory</a>

The "famous" Hubbard model was conceived in the 1960s [1,2,3] to get
insight into how the Coulomb interactions between conduction electrons
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<img src="/img/DGontier.jpg" width="600">

### Mauricio Rodríguez-Mayorga (Neel Institute, Grenoble)
### Mauricio Rodríguez-Mayorga (Neel Institute, Grenoble) & Mi-Song Dupuy (LJLL, Paris)

**Relativistic effects on the two-electron Harmonium atom**
<a href="/presentations/MDupuy.pdf">Harmonium: a model to study approximations in TDDFT</a> (by Mi-Song Dupuy)

**Relativistic effects on the two-electron Harmonium atom** (by Mauricio Rodríguez-Mayorga)

The non-relativistic Harmonium atom is a model system where parabolic confinement ($1⁄2\omega^2 r^2$) replaces the Coulombic ($-Z/r$) electron-nucleus interaction [1-4]. Varying the confinement strength (ω) enhances the different types of electronic correlation effects. Large (small) ω values make the weak (strong) electronic correlation dominant [1,3]. Consequently, this model system has served as a tool in the development and benchmarking of methods [5,6]. Moreover, analytic solutions for the two-electron Harmonium atom can also be obtained for certain ω values [4], which provides us with wavefunctions for two electrons that are explored to better understand the repercussions of electronic correlation effects.
In this work, we explore numerically the role of relativistic effects on the two-electron Harmonium. Our results indicate that only for the large $\omega$ values scalar relativistic effects are important and lead to a reduction of the total energy accompanied by changes in the electronic structure (e.g. a shrinking of the radial electronic density P(r)).
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64 changes: 40 additions & 24 deletions static/mini_program/mini.tex
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\begin{document}
\section*{Thursday, January 11, 2024}

\begin{tabular}{llp{15cm}}
\begin{tabular}{|l|l|p{15cm}|}
\hline
TIME & SPEAKER & TITLE \\
9:00 - 9:30 & \emoji{wave} Welcome \\
& \\
SESSION 1 & \emoji{thinking} Chair: Julien Toulouse \\
9:30 - 10:00 & Lucia Reining & Zero, one, many: the Hubbard dimer with two electrons in many-body perturbation theory \\
\hline
9:00 - 9:30 & \emoji{wave} Welcome \& Poster &\\
& & \\
\hline
SESSION 1 & \emoji{thinking} Chair: Julien Toulouse &\\
& & \\
9:30 - 10:00 & Lucia Reining & Zero, one, many: the Hubbard dimer with two electrons in many-body perturbation theory \\
10:00 - 10:30 & Bruno Senjean & Site-occupation embedding theory and ensemble density functional theory on the Hubbard dimer \\
10:30 - 11:00 & \emoji{coffee} Coffee break \& Poster \\
10:30 - 11:00 & \emoji{coffee} Coffee break \& Poster & \\
11:00 - 11:30 & Eric Cancès & Model systems for discretization error analysis \\
11:30 - 12:00 & Diata Traore & One-dimensional model systems for understanding and development of the density-based basis-set correction method \\
12:00 - 12:30 & Timothee Audinet & One-dimensional model with delta-type interactions: Dirac’s equation with QED interactions \\
& \\
12:30 - 14:00 & \emoji{green-salad} Lunch break \& Poster \\
& \\
SESSION 2 &\emoji{thinking} Chair: Mi-Song Dupuy \\
14:00 - 14:30 & Nicolas Laflorencie & Topological and quantum critical properties of the interacting Majorana chain model \\
\hline
& & \\
12:30 - 14:00 & \emoji{green-salad} Lunch break \& Poster & \\
& & \\
\hline
SESSION 2 &\emoji{thinking} Chair: Mi-Song Dupuy &\\
& & \\
14:00 - 14:30 & Nicolas Laflorencie & Topological and quantum critical properties of the interacting Majorana chain model \\
14:30 - 15.00 & Arjan Berger & The one-point model: solving equations in pointland \\
15:30 - 16:00 & \emoji{coffee} Coffee break \& Poster \\
15:30 - 16:00 & \emoji{coffee} Coffee break \& Poste & \\
16:00 - 16:30 & Peter Gill & Finite Uniform Electron Gases \\
16:30 - 17.00 & Mauricio Rodríguez-Mayorga & Relativistic effects on the two-electron Harmonium atom \\
17:00 - 17.30 & Michel Caffarel & Path integral for the quartic oscillator: An approximate analytic expression for the partition function \\
% & \\
% 17:30 - 18:30 & \emoji{beers} Cocktail \& Poster \\
% 19:30 - 22:30 & \emoji{fork-and-knife} Dinner "Chez Navarre" & 49 Grand Rue Nazareth, Toulouse \\
\hline
\end{tabular}

\section*{Friday, January 12, 2024}

\begin{tabular}{llp{15cm}}
\begin{tabular}{|l|l|p{15cm}|}
\hline
TIME & SPEAKER & TITLE \\
9:00 - 9:30 & \emoji{wave} Welcome \\
& \\
SESSION 3 & \emoji{thinking} Chair: Thomas Duguet \\
\hline
9:00 - 9:30 & \emoji{wave} Welcome \& Poster & \\
& & \\
\hline
SESSION 3 & \emoji{thinking} Chair: Thomas Duguet & \\
& & \\
9:30 - 10:00 & Marie Labeye & Time dependent models for strong field physics \\
10:00 - 10:30 & Umberto Morellini & Relativistic electrons coupled with Newtonian nuclear dynamics \\
10:30 - 11:00 & \emoji{coffee} Coffee break \& Poster \\
10:30 - 11:00 & \emoji{coffee} Coffee break \& Poster & \\
11:00 - 11:30 & Alexander Tichai & Nuclear superfluidity: the Pairing Hamiltonian as a many-body testbed \\
11:30 - 12:00 & Denis Lacroix & Exploring the richness of the Lipkin Model and its extensions: from nuclear to neutrino physics and quantum computing \\
12:00 - 12:30 & Antoine Levitt & Resonances: the example of the 1D chain \\
& \\
12:30 - 14:00 & \emoji{green-salad} Lunch break \& Poster \\
& \\
SESSION 4 & \emoji{thinking} Chair: Eleonora Luppi \\
12:00 - 12:30 & David Gontier & Phase transition in the Peierls / SSH model \\
\hline
& & \\
12:30 - 14:00 & \emoji{green-salad} Lunch break \& Poster & \\
& & \\
\hline
SESSION 4 & \emoji{thinking} Chair: Eleonora Luppi & \\
& & \\
14:00 - 14:30 & Cyril Martins & An introduction to Dynamical Mean-Field Theory \\
14:30 - 15.00 & Alfred Kirsch & Some mathematical insights on DMFT on a Hubbard model \\
15:30 - 16:00 & \emoji{coffee} Coffee break \& Poster \\
15:30 - 16:00 & \emoji{coffee} Coffee break \& Poster & \\
16:00 - 16:30 & Aleksandra Petkovic & Dissipative impurity dynamics in one dimensional quantum liquids \\
16:30 - 17.00 & David Gontier & Phase transition in the Peierls / SSH model \\
16:30 - 17.00 & Antoine Levitt & Resonances: the example of the 1D chain \\
% 17:00 - 17.30 & Antoine Levitt & Resonances: the example of the 1D chain \\
% & \\
% 17:30 - 18:30 & \emoji{champagne} Cocktail \& Poster \\
% 19:30 - 22:30 & \emoji{moai} Dinner at "Le Moa\"i" & 35 All\'ee Jules Guesde, Toulouse\\
\hline
\end{tabular}

%\begin{center}
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