Algebraic Bethe Ansatz And Correlation Functions: An Advanced Course

Algebraic Bethe Ansatz And Correlation Functions: An Advanced Course

Author: Nikita Slavnov

Publisher: World Scientific

Published: 2022-05-12

Total Pages: 399

ISBN-13: 9811254273

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It is unlikely that today there is a specialist in theoretical physics who has not heard anything about the algebraic Bethe ansatz. Over the past few years, this method has been actively used in quantum statistical physics models, condensed matter physics, gauge field theories, and string theory.This book presents the state-of-the-art research in the field of algebraic Bethe ansatz. Along with the results that have already become classic, the book also contains the results obtained in recent years. The reader will get acquainted with the solution of the spectral problem and more complex problems that are solved using this method. Various methods for calculating scalar products and form factors are described in detail. Special attention is paid to applying the algebraic Bethe ansatz to the calculation of the correlation functions of quantum integrable models. The book also elaborates on multiple integral representations for correlation functions and examples of calculating the long-distance asymptotics of correlations.This text is intended for advanced undergraduate and postgraduate students, and specialists interested in the mathematical methods of studying physical systems that allow them to obtain exact results.


Book Synopsis Algebraic Bethe Ansatz And Correlation Functions: An Advanced Course by : Nikita Slavnov

Download or read book Algebraic Bethe Ansatz And Correlation Functions: An Advanced Course written by Nikita Slavnov and published by World Scientific. This book was released on 2022-05-12 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is unlikely that today there is a specialist in theoretical physics who has not heard anything about the algebraic Bethe ansatz. Over the past few years, this method has been actively used in quantum statistical physics models, condensed matter physics, gauge field theories, and string theory.This book presents the state-of-the-art research in the field of algebraic Bethe ansatz. Along with the results that have already become classic, the book also contains the results obtained in recent years. The reader will get acquainted with the solution of the spectral problem and more complex problems that are solved using this method. Various methods for calculating scalar products and form factors are described in detail. Special attention is paid to applying the algebraic Bethe ansatz to the calculation of the correlation functions of quantum integrable models. The book also elaborates on multiple integral representations for correlation functions and examples of calculating the long-distance asymptotics of correlations.This text is intended for advanced undergraduate and postgraduate students, and specialists interested in the mathematical methods of studying physical systems that allow them to obtain exact results.

Physics and Mathematics of Quantum Many-Body Systems

Physics and Mathematics of Quantum Many-Body Systems

Author: Hal Tasaki

Publisher: Springer Nature

Published: 2020-05-07

Total Pages: 534

ISBN-13: 3030412652

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This book is a self-contained advanced textbook on the mathematical-physical aspects of quantum many-body systems, which begins with a pedagogical presentation of the necessary background information before moving on to subjects of active research, including topological phases of matter. The book explores in detail selected topics in quantum spin systems and lattice electron systems, namely, long-range order and spontaneous symmetry breaking in the antiferromagnetic Heisenberg model in two or higher dimensions (Part I), Haldane phenomena in antiferromagnetic quantum spin chains and related topics in topological phases of quantum matter (Part II), and the origin of magnetism in various versions of the Hubbard model (Part III). Each of these topics represents certain nontrivial phenomena or features that are invariably encountered in a variety of quantum many-body systems, including quantum field theory, condensed matter systems, cold atoms, and artificial quantum systems designed for future quantum computers. The book’s main focus is on universal properties of quantum many-body systems. The book includes roughly 50 problems with detailed solutions. The reader only requires elementary linear algebra and calculus to comprehend the material and work through the problems. Given its scope and format, the book is suitable both for self-study and as a textbook for graduate or advanced undergraduate classes.


Book Synopsis Physics and Mathematics of Quantum Many-Body Systems by : Hal Tasaki

Download or read book Physics and Mathematics of Quantum Many-Body Systems written by Hal Tasaki and published by Springer Nature. This book was released on 2020-05-07 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a self-contained advanced textbook on the mathematical-physical aspects of quantum many-body systems, which begins with a pedagogical presentation of the necessary background information before moving on to subjects of active research, including topological phases of matter. The book explores in detail selected topics in quantum spin systems and lattice electron systems, namely, long-range order and spontaneous symmetry breaking in the antiferromagnetic Heisenberg model in two or higher dimensions (Part I), Haldane phenomena in antiferromagnetic quantum spin chains and related topics in topological phases of quantum matter (Part II), and the origin of magnetism in various versions of the Hubbard model (Part III). Each of these topics represents certain nontrivial phenomena or features that are invariably encountered in a variety of quantum many-body systems, including quantum field theory, condensed matter systems, cold atoms, and artificial quantum systems designed for future quantum computers. The book’s main focus is on universal properties of quantum many-body systems. The book includes roughly 50 problems with detailed solutions. The reader only requires elementary linear algebra and calculus to comprehend the material and work through the problems. Given its scope and format, the book is suitable both for self-study and as a textbook for graduate or advanced undergraduate classes.

Physics Letters

Physics Letters

Author:

Publisher:

Published: 1997

Total Pages: 452

ISBN-13:

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Book Synopsis Physics Letters by :

Download or read book Physics Letters written by and published by . This book was released on 1997 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The One-Dimensional Hubbard Model

The One-Dimensional Hubbard Model

Author: Fabian H. L. Essler

Publisher: Cambridge University Press

Published: 2005-02-07

Total Pages: 692

ISBN-13: 1139441582

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This book presents an account of the exact solution of the Hubbard model in one dimension. The early chapters develop a self-contained introduction to Bethe's ansatz and its application to the one-dimensional Hubbard model. The later chapters address more advanced topics.


Book Synopsis The One-Dimensional Hubbard Model by : Fabian H. L. Essler

Download or read book The One-Dimensional Hubbard Model written by Fabian H. L. Essler and published by Cambridge University Press. This book was released on 2005-02-07 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an account of the exact solution of the Hubbard model in one dimension. The early chapters develop a self-contained introduction to Bethe's ansatz and its application to the one-dimensional Hubbard model. The later chapters address more advanced topics.

Quantum Inverse Scattering Method and Correlation Functions

Quantum Inverse Scattering Method and Correlation Functions

Author: V. E. Korepin

Publisher: Cambridge University Press

Published: 1997-03-06

Total Pages: 582

ISBN-13: 9780521586467

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The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.


Book Synopsis Quantum Inverse Scattering Method and Correlation Functions by : V. E. Korepin

Download or read book Quantum Inverse Scattering Method and Correlation Functions written by V. E. Korepin and published by Cambridge University Press. This book was released on 1997-03-06 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.

The Hubbard Model

The Hubbard Model

Author: Dionys Baeriswyl

Publisher: Springer Science & Business Media

Published: 2013-11-11

Total Pages: 408

ISBN-13: 1489910425

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In the slightly more than thirty years since its formulation, the Hubbard model has become a central component of modern many-body physics. It provides a paradigm for strongly correlated, interacting electronic systems and offers insights not only into the general underlying mathematical structure of many-body systems but also into the experimental behavior of many novel electronic materials. In condensed matter physics, the Hubbard model represents the simplest theoret ical framework for describing interacting electrons in a crystal lattice. Containing only two explicit parameters - the ratio ("Ujt") between the Coulomb repulsion and the kinetic energy of the electrons, and the filling (p) of the available electronic band - and one implicit parameter - the structure of the underlying lattice - it appears nonetheless capable of capturing behavior ranging from metallic to insulating and from magnetism to superconductivity. Introduced originally as a model of magnetism of transition met als, the Hubbard model has seen a spectacular recent renaissance in connection with possible applications to high-Tc superconductivity, for which particular emphasis has been placed on the phase diagram of the two-dimensional variant of the model. In mathematical physics, the Hubbard model has also had an essential role. The solution by Lieb and Wu of the one-dimensional Hubbard model by Bethe Ansatz provided the stimulus for a broad and continuing effort to study "solvable" many-body models. In higher dimensions, there have been important but isolated exact results (e. g. , N agoaka's Theorem).


Book Synopsis The Hubbard Model by : Dionys Baeriswyl

Download or read book The Hubbard Model written by Dionys Baeriswyl and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the slightly more than thirty years since its formulation, the Hubbard model has become a central component of modern many-body physics. It provides a paradigm for strongly correlated, interacting electronic systems and offers insights not only into the general underlying mathematical structure of many-body systems but also into the experimental behavior of many novel electronic materials. In condensed matter physics, the Hubbard model represents the simplest theoret ical framework for describing interacting electrons in a crystal lattice. Containing only two explicit parameters - the ratio ("Ujt") between the Coulomb repulsion and the kinetic energy of the electrons, and the filling (p) of the available electronic band - and one implicit parameter - the structure of the underlying lattice - it appears nonetheless capable of capturing behavior ranging from metallic to insulating and from magnetism to superconductivity. Introduced originally as a model of magnetism of transition met als, the Hubbard model has seen a spectacular recent renaissance in connection with possible applications to high-Tc superconductivity, for which particular emphasis has been placed on the phase diagram of the two-dimensional variant of the model. In mathematical physics, the Hubbard model has also had an essential role. The solution by Lieb and Wu of the one-dimensional Hubbard model by Bethe Ansatz provided the stimulus for a broad and continuing effort to study "solvable" many-body models. In higher dimensions, there have been important but isolated exact results (e. g. , N agoaka's Theorem).

Tensor Network Contractions

Tensor Network Contractions

Author: Shi-Ju Ran

Publisher: Springer Nature

Published: 2020-01-27

Total Pages: 160

ISBN-13: 3030344894

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Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.


Book Synopsis Tensor Network Contractions by : Shi-Ju Ran

Download or read book Tensor Network Contractions written by Shi-Ju Ran and published by Springer Nature. This book was released on 2020-01-27 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Tensor network is a fundamental mathematical tool with a huge range of applications in physics, such as condensed matter physics, statistic physics, high energy physics, and quantum information sciences. This open access book aims to explain the tensor network contraction approaches in a systematic way, from the basic definitions to the important applications. This book is also useful to those who apply tensor networks in areas beyond physics, such as machine learning and the big-data analysis. Tensor network originates from the numerical renormalization group approach proposed by K. G. Wilson in 1975. Through a rapid development in the last two decades, tensor network has become a powerful numerical tool that can efficiently simulate a wide range of scientific problems, with particular success in quantum many-body physics. Varieties of tensor network algorithms have been proposed for different problems. However, the connections among different algorithms are not well discussed or reviewed. To fill this gap, this book explains the fundamental concepts and basic ideas that connect and/or unify different strategies of the tensor network contraction algorithms. In addition, some of the recent progresses in dealing with tensor decomposition techniques and quantum simulations are also represented in this book to help the readers to better understand tensor network. This open access book is intended for graduated students, but can also be used as a professional book for researchers in the related fields. To understand most of the contents in the book, only basic knowledge of quantum mechanics and linear algebra is required. In order to fully understand some advanced parts, the reader will need to be familiar with notion of condensed matter physics and quantum information, that however are not necessary to understand the main parts of the book. This book is a good source for non-specialists on quantum physics to understand tensor network algorithms and the related mathematics.

Condensed Matter Field Theory

Condensed Matter Field Theory

Author: Alexander Altland

Publisher: Cambridge University Press

Published: 2010-03-11

Total Pages: 785

ISBN-13: 0521769752

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This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.


Book Synopsis Condensed Matter Field Theory by : Alexander Altland

Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.

Non-Perturbative Field Theory

Non-Perturbative Field Theory

Author: Yitzhak Frishman

Publisher: Cambridge University Press

Published: 2010-04-08

Total Pages: 455

ISBN-13: 1139486489

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Providing a new perspective on quantum field theory, this book is useful for graduate students and researchers within and outside the field. It describes non-perturbative methods, and explores two-dimensional and four-dimensional gauge dynamics using those methods. Applications are thoroughly described.


Book Synopsis Non-Perturbative Field Theory by : Yitzhak Frishman

Download or read book Non-Perturbative Field Theory written by Yitzhak Frishman and published by Cambridge University Press. This book was released on 2010-04-08 with total page 455 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a new perspective on quantum field theory, this book is useful for graduate students and researchers within and outside the field. It describes non-perturbative methods, and explores two-dimensional and four-dimensional gauge dynamics using those methods. Applications are thoroughly described.

Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory

Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory

Author: S. Pakuliak

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 334

ISBN-13: 9401006709

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Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.


Book Synopsis Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory by : S. Pakuliak

Download or read book Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory written by S. Pakuliak and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.