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Dynamics of Many-Body Quantum Systems

Aleix Gimenez-Grau

Published Jul 3, 2015• 0 citations
OpenAlex

Abstract

Interacting many-body quantum systems are in general difficult to treat. Getting an accurate description of the ground state of a many-body system is hard but standard techniques based on Monte Carlo methods are available. Getting the spectrum of elementary excitations is more involved, and approximation techniques based on elaborated perturbative approaches are in order. In the work the student will have to learn and use the theory of Corrlated Basis Functions, which allows for a reliable estimation of the dynamic structure function of a system of bosons.

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Interacting many-body quantum systems are in general difficult to treat. Getting an accurate description of the ground state of a many-body system is hard but standard techniques based on Monte Carlo methods are available. Getting the spectrum of elementary excitations is more involved, and approximation techniques based on elaborated perturbative approaches are in order. In the work the student will have to learn and use the theory of Corrlated Basis Functions, which allows for a reliable estimation of the dynamic structure function of a system of bosons.
Recent progress in the theory and computation of electronic structure is bringing an unprecedented level of capability for research. Many-body methods are becoming essential tools vital for quantitative calculations and understanding materials phenomena in physics, chemistry, materials science and other fields. This book provides a unified exposition of the most-used tools: many-body perturbation theory, dynamical mean field theory and quantum Monte Carlo simulations. Each topic is introduced with a less technical overview for a broad readership, followed by in-depth descriptions and mathematical formulation. Practical guidelines, illustrations and exercises are chosen to enable readers to appreciate the complementary approaches, their relationships, and the advantages and disadvantages of each method. This book is designed for graduate students and researchers who want to use and understand these advanced computational tools, get a broad overview, and acquire a basis for participating in new developments.
Recent progress in the theory and computation of electronic structure is bringing an unprecedented level of capability for research. Many-body methods are becoming essential tools vital for quantitative calculations and understanding materials phenomena in physics, chemistry, materials science and other fields. This book provides a unified exposition of the most-used tools: many-body perturbation theory, dynamical mean field theory and quantum Monte Carlo simulations. Each topic is introduced with a less technical overview for a broad readership, followed by in-depth descriptions and mathematical formulation. Practical guidelines, illustrations and exercises are chosen to enable readers to appreciate the complementary approaches, their relationships, and the advantages and disadvantages of each method. This book is designed for graduate students and researchers who want to use and understand these advanced computational tools, get a broad overview, and acquire a basis for participating in new developments.
Interacting many-body quantum systems are in general difficult to treat. Getting an accurate description of the ground state of a many-body system is hard but standard techniques based on Monte Carlo methods are available. Getting the spectrum of elementary excitations is more involved, and approximation techniques based on elaborated perturbative approaches are in order. In the work the student will have to learn and use the theory of Corrlated Basis Functions, which allows for a reliable estimation of the dynamic structure function of a system of bosons.
The interaction among fundamental particles in nature leads to many interesting effects in quantum statistical mechanics; examples include superconductivity for charged systems and superfluidity in cold gases. It is a huge challenge for mathematical physics to understand the collective behavior of systems containing a large number of particles, emerging from known microscopic interactions. In this workshop we brought together researchers working on different aspects of many-body quantum mechanics to discuss recent developments, exchange ideas and propose new challenges and research directions.
In this work we introduce the dual boson diagrammatic Monte Carlo technique for strongly interacting electronic systems. This method combines the strength of dynamical mean-filed theory for nonperturbative description of local correlations with the systematic account of nonlocal corrections in the dual boson theory by the diagrammatic Monte Carlo approach. It allows us to get a numerically exact solution of the dual boson theory at the two-particle local vertex level for the extended Hubbard model. We show that it can be efficiently applied to description of single-particle observables in a wide range of interaction strengths. We compare our exact results for the self-energy with the ladder dual boson approach and determine a physical regime, where the description of collective electronic effects requires more accurate consideration beyond the ladder approximation. Additionally, we find that the order-by-order analysis of the perturbative diagrammatic series for the single-particle Green's function allows to estimate the transition point to the charge density wave phase.