04007nam a22005415i 4500 978-3-031-47233-6 DE-He213 20251030110910.0 cr nn 008mamaa 240103s2024 sz | s |||| 0|eng d 9783031472336 978-3-031-47233-6 10.1007/978-3-031-47233-6 doi QC173.96-174.52 PHQ bicssc SCI057000 bisacsh PHQ thema Debertolis, Maxime. author. aut http://id.loc.gov/vocabulary/relators/aut 69009 Quantum Impurity Problems in the Framework of Natural Orbitals [electronic resource] : A Comprehensive Study / by Maxime Debertolis. 1st ed. 2024. Cham : Springer Nature Switzerland : Imprint: Springer, 2024. XV, 165 p. 48 illus. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5061 The Quantum Impurity Problem -- IRLM and Kondo Correlations -- Few-body Nature of Kondo Correlated Ground States -- Recursive generation of Natural Orbitals -- RGNO Study of Screening Clouds in Disordered Environments. This book presents a complete study of natural orbitals in quantum impurity problems, revealing a certain simplicity in these interacting many-body problems. These systems consist of a few localized degrees of freedom that undergo strong interactions and hybridize with a larger system of free particles; they are central in the study of strongly correlated systems. In a first step, the standard non-perturbative numerical renormalization group method is employed to demonstrate the hierarchical structure of correlations unveiled by natural orbitals. This simplification brought new insights for simulating quantum impurity problems, and a new algorithm is developed to generate an optimized subset of natural orbitals independently of existing methods, going beyond their usual limitations. This algorithm is presented in detail in the book, and a careful benchmark on known results is carried out to guarantee the validity of the method. It is then used to study spatialentanglement structures under various conditions that were not accessible with previous methods, such as representing the electron bath by a realistic 2D square lattice or taking account of static disorder in the metallic host. In the last chapter, the non-interacting problem in the presence of disorder is studied through random matrix theory, reproducing some of the results presented in the previous chapters. The main original result of this chapter lies in the analytical calculation of the joint distribution of one-particle orbitals energies and amplitudes of the impurity, which makes it possible to calculate any disordered averaged local correlation functions. Starting from this result, calculations in the large-N limit are compared with numerical simulations. Quantum physics. 66608 Electronics Materials. 67189 Quantum entanglement. 69010 Quantum Physics. 66608 Electronic Materials. 67191 Quantum Correlation and Entanglement. 69011 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031472329 Printed edition: 9783031472343 Printed edition: 9783031472350 Springer Theses, Recognizing Outstanding Ph.D. Research, 2190-5061 66370 https://doi.org/10.1007/978-3-031-47233-6 ZDB-2-PHA ZDB-2-SXP 57032 57032