My PhD thesis presents three applications of machine learning to condensed matter theory. Firstly, I will explain how the problem of detecting phase transitions can be rephrased as an image classification task, paving the way to the automatic mapping of phase diagrams. I tested the reliability of this approach and showed its limits for models exhibiting a many-body localized phase in 1 and 2 dimensions. Secondly, I will introduce a variational representation of quantum many-body ground-states in the form of neural-networks and show our results on a constrained model of hardcore bosons in 2d using variational and projection methods. In particular, we confirmed the phase diagram obtained independently earlier and extends its validity to larger system sizes. Moreover we also established the ability of neural-network quantum states to approximate accurately solid and liquid bosonic phases of matter. Finally, I will present a new approach to quantum error correction based on the same techniques used to conceive the best Go game engine. We showed that efficient correction strategies can be uncovered with evolutionary optimization algorithms, competitive with gradient-based optimization techniques. In particular, we found that shallow neural-networks are competitive with deep neural-networks.

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A novel approach for the synthesis of Fe(0) nanoparticles (NPs) with tunable sizes and shapes is reported. Ultrasmall Fe(0) NPs were reacted under mild conditions in the presence of a mixture of palmitic acid and amine ligands. These NPs acted not only as preformed seeds but also as an internal iron(II) source that was produced by the partial dissolution of the NPs by the acid. This fairly simple approach allows a strict separation between the nucleation and the growth steps. By changing the acid concentration, a fine tuning of the relative ratio between remaining Fe(0) seeds and iron(II) reservoir was achieved, giving access to both size (from 7 to 20 nm) and a shape (spheres, cubes or stars) control. The partial dissolution of the ultrasmall Fe(0) NPs into iron(II) source and the successive growth was further studied by using combined TEM and Mössbauer spectroscopy. The successive corrosion, coalescence, and ripening observed could be understood in the framework of an environment-dependent growth model.

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Single crystalline FeCo nanoparticles with tunable size and shape were prepared by co-decomposing two metal-amide precursors under mild conditions. The nature of the ligands introduced in this organometallic synthesis drastically affects the reactivity of the precursors and thus the chemical distribution within the nanoparticles. The presence of the B2 short-range order was evidenced in FeCo nanoparticles prepared in presence of HDAHCl ligands, combining 57 Fe Mössbauer, zero field 59 Co Ferromagnetic Nuclear Resonance (FNR) and X-ray diffraction studies. This is the first time that the B2 structure is directly formed during synthesis without the need of any annealing step. The as-prepared nanoparticles exhibit magnetic properties comparable with the ones of the bulk (Ms = 226 Am².kg-1). Composite magnetic materials prepared from these FeCo nanoparticles led to a successful proof-of-concept of integration on inductor-based filters (27% enhancement of the inductance value at 100 MHz).

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Selected configuration interaction (sCI) methods, when complemented with a second order perturbative correction , provide near full configuration interaction (FCI) quality energies with only a small fraction of the Slater determinants of the FCI space. The selection of the determinants is often implemented in a determinant-based formalism, and therefore does not provide spin adapted wave functions. In other words, sCI wave functions are not eigenfunctions of theŜ 2 operator. In some situations, having a spin adapted wave function is essential for the proper convergence of the method. We propose an efficient algorithm which, given an arbitrary determinant space, generates all the missing Slater determinants allowing one to obtain spin adapted wave functions while avoiding working with configuration state functions. For example, generating all the possible determinants with 6 up-spin and 6 down-spin electrons in 12 open shells takes 21 CPU cycles per generated Slater determinant. We also propose a modification of the denominators in the Epstein-Nesbet perturbation theory reducing significantly the non-invariance of the second order correction with respect to different values of the spin quantum number m s. The computational cost of this correction is also negligible.

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Les nanomatériaux hybrides organique-inorganique (nanocomposites) connaissent un intérêt croissant notamment grâce au développement de nouvelles méthodes permettant leur synthèse. Afin de moduler leurs propriétés, il est important de contrôler la nature chimique des constituants ainsi que leurs interactions. Dans le cadre de ce travail de thèse, nous avons mis en évidence une nouvelle approche de croissance et de structuration de nanoparticules métalliques (Pt, Ir, Au, etc.) en utilisant des polymères peptidiques comme ligands macromoléculaires. A l'instar des protéines, ces derniers sont constitués d'acides aminés et adoptent certaines structurations biomimétiques (hélice α ou feuillet β), un élément peu étudié pour promouvoir des nanocomposites.Ce travail commence par un travail de synthèse consistant à préparer une librairie de polymères peptidiques incorporant des points d'ancrage chimiques pour moduler leur association à des particules métalliques. Nous avons pour cela développé des réactions de greffage sur du poly(γ-benzyl-L-glutamate) (PBLG) avec différentes amines fonctionnalisées pour promouvoir une chimie de coordination spécifique avec les métaux de transitions.La deuxième partie de ce manuscrit décrit ensuite l'utilisation de ces polymères peptidiques comme matrice permettant la croissance contrôlée de nanoparticules métalliques (synthèse in situ). Nous avons ainsi mis en évidence que les polypeptides donnent accès à des nanoparticules hyperbranchées, résultant de la coalescence de nanocristaux ultra-petits, dont la morphologie peut être contrôlée en jouant sur les propriétés du polymère (degré de polymérisation, stœchiométrie des chaines latérales).Dans une dernière partie, les polymères peptidiques ont finalement été utilisés pour guider l'autoassemblage de nanoparticules métalliques préformées. Nous avons ainsi obtenu des structures lamellaires bidimensionnelles, dont la stabilité est assurée par des liaisons de coordination spécifiques entre les groupements fonctionnels du polymère et la surface des nanoparticules. En modulant la taille des polymères, il a été possible de contrôler l’espace entre les lamelles, une modification structurale clé qui permet de modifier les propriétés électriques des nanocomposites.

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