LEADER 03846nam 22005895 450 001 9910799485003321 005 20240321220149.0 010 $a9783031472336 010 $a3031472330 024 7 $a10.1007/978-3-031-47233-6 035 $a(CKB)29526983300041 035 $a(MiAaPQ)EBC31071236 035 $a(Au-PeEL)EBL31071236 035 $a(DE-He213)978-3-031-47233-6 035 $a(OCoLC)1416923359 035 $a(EXLCZ)9929526983300041 100 $a20240103d2024 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aQuantum Impurity Problems in the Framework of Natural Orbitals $eA Comprehensive Study /$fby Maxime Debertolis 205 $a1st ed. 2024. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Springer,$d2024. 215 $a1 online resource (170 pages) 225 1 $aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5061 311 08$a9783031472329 327 $aThe 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. 330 $aThis book presents a complete study of natural orbitals in quantum impurity problems, revealing a certain simplicity in these interacting many-body problems. These systems consist of a few localized degrees of freedom that undergo strong interactions and hybridize with a larger system of free particles; they are central in the study of strongly correlated systems. In a first step, the standard non-perturbative numerical renormalization group method is employed to demonstrate the hierarchical structure of correlations unveiled by natural orbitals. This simplification brought new insights for simulating quantum impurity problems, and a new algorithm is developed to generate an optimized subset of natural orbitals independently of existing methods, going beyond their usual limitations. This algorithm is presented in detail in the book, and a careful benchmark on known results is carried out to guarantee the validity of the method. It is then used to study spatialentanglement structures under various conditions that were not accessible with previous methods, such as representing the electron bath by a realistic 2D square lattice or taking account of static disorder in the metallic host. In the last chapter, the non-interacting problem in the presence of disorder is studied through random matrix theory, reproducing some of the results presented in the previous chapters. The main original result of this chapter lies in the analytical calculation of the joint distribution of one-particle orbitals energies and amplitudes of the impurity, which makes it possible to calculate any disordered averaged local correlation functions. Starting from this result, calculations in the large-N limit are compared with numerical simulations. 410 0$aSpringer Theses, Recognizing Outstanding Ph.D. Research,$x2190-5061 606 $aQuantum theory 606 $aElectronics$xMaterials 606 $aQuantum entanglement 606 $aQuantum Physics 606 $aElectronic Materials 606 $aQuantum Correlation and Entanglement 615 0$aQuantum theory. 615 0$aElectronics$xMaterials. 615 0$aQuantum entanglement. 615 14$aQuantum Physics. 615 24$aElectronic Materials. 615 24$aQuantum Correlation and Entanglement. 676 $a530.12 700 $aDebertolis$b Maxime$01586363 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910799485003321 996 $aQuantum Impurity Problems in the Framework of Natural Orbitals$93872751 997 $aUNINA