Quantum Impurity Problems in the Framework of Natural Orbitals: A Comprehensive Study

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Maxime Debertolis

Quantum Impurity Problems in the Framework of Natural Orbitals

A Comprehensive Study

Maxime Debertolis

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English

Springer International Publishing AG
04 January 2024

Quantum physics (quantum mechanics & quantum field theory); Chemistry; Mechanical engineering; Other technologies & applied sciences

Series: Springer Theses

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.

By: Maxime Debertolis
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 2024 ed.
Dimensions: Height: 235mm, Width: 155mm,
Weight: 448g
ISBN: 9783031472329
ISBN 10: 3031472322
Series: Springer Theses
Pages: 165
Publication Date: 04 January 2024
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Maxime Debertolis received his PhD in theoretical Condensed Matter physics in 2022 under the supervision of S. Florens at Néel Institute (CNRS) in Grenoble, France. His PhD research was focused on the study of quantum impurity problems, which are central to the field of condensed matter. During his thesis, he proposed a new method to simulate these problems at equilibrium, which has opened up new perspectives for future work in this field. He is currently working as a postdoctoral researcher in the group of D. Luitz at Bonn University, Germany, on theoretical quantum many-problems and quantum simulation, linking problems of condensed matter to the current development of digital quantum computers.