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Quantum impurity problems in the framework of natural orbitals = a comprehensive study /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Quantum impurity problems in the framework of natural orbitals/ by Maxime Debertolis.
Reminder of title:	a comprehensive study /
Author:	Debertolis, Maxime.
Published:	Cham :Springer Nature Switzerland : : 2024.,
Description:	xv, 165 p. :ill., digital ;24 cm.
Notes:	"Doctoral thesis accepted by The Université Grenoble Alpes, Grenoble, France."
[NT 15003449]:	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.
Contained By:	Springer Nature eBook
Subject:	Many-body problem. -
Online resource:	https://doi.org/10.1007/978-3-031-47233-6
ISBN:	9783031472336

Quantum impurity problems in the framework of natural orbitals = a comprehensive study /
Debertolis, Maxime.

Quantum impurity problems in the framework of natural orbitalsa comprehensive study /[electronic resource] :by Maxime Debertolis. - Cham :Springer Nature Switzerland :2024. - xv, 165 p. :ill., digital ;24 cm. - Springer theses,2190-5061. - Springer theses..

"Doctoral thesis accepted by The Université Grenoble Alpes, Grenoble, France."

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 spatial entanglement 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.

ISBN: 9783031472336

Standard No.: 10.1007/978-3-031-47233-6doiSubjects--Topical Terms:

525019
Many-body problem.

LC Class. No.: QC174.17.P7

Dewey Class. No.: 530.144

Quantum impurity problems in the framework of natural orbitals = a comprehensive study /
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245 1 0 $a Quantum impurity problems in the framework of natural orbitals $h [electronic resource] : $b a comprehensive study / $c by Maxime Debertolis.
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490 1 $a Springer theses, $x 2190-5061
500 $a "Doctoral thesis accepted by The Université Grenoble Alpes, Grenoble, France."
505 0 $a 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.
520 $a 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 spatial entanglement 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.
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