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Off-Diagonal Bethe Ansatz for Exactly Solvable Models

Author: Yupeng Wang

Publisher: Springer

Published: 2015-04-21

Total Pages: 303

ISBN-13: 3662467569

This book serves as an introduction of the off-diagonal Bethe Ansatz method, an analytic theory for the eigenvalue problem of quantum integrable models. It also presents some fundamental knowledge about quantum integrability and the algebraic Bethe Ansatz method. Based on the intrinsic properties of R-matrix and K-matrices, the book introduces a systematic method to construct operator identities of transfer matrix. These identities allow one to establish the inhomogeneous T-Q relation formalism to obtain Bethe Ansatz equations and to retrieve corresponding eigenstates. Several longstanding models can thus be solved via this method since the lack of obvious reference states is made up. Both the exact results and the off-diagonal Bethe Ansatz method itself may have important applications in the fields of quantum field theory, low-dimensional condensed matter physics, statistical physics and cold atom systems.

An Introduction to Integrable Techniques for One-Dimensional Quantum Systems

Author: Fabio Franchini

Publisher: Springer

Published: 2017-05-25

Total Pages: 180

ISBN-13: 3319484877

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This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.

Exactly Solvable Models Of Strongly Correlated Electrons

Author: Fabian H L Essler

Publisher: World Scientific

Published: 1994-05-24

Total Pages: 504

ISBN-13: 981450274X

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Systems of strongly correlated electrons are at the heart of recent developments in condensed matter theory. They have applications to phenomena like high-Tc superconductivity and the fractional quantum hall effect. Analytical solutions to such models, though mainly limited to one spatial dimension, provide a complete and unambiguous picture of the dynamics involved. This volume is devoted to such solutions obtained using the Bethe Ansatz, and concentrates on the most important of such models, the Hubbard model. The reprints are complemented by reviews at the start of each chapter and an extensive bibliography.

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.

Festschrift In Honor Of The C N Yang Centenary, A: Scientific Papers

Author: Fong-ching Chen

Publisher: World Scientific

Published: 2022-08-03

Total Pages: 638

ISBN-13: 9811264163

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C N Yang is a towering figure of science who has significantly extended human understanding of nature, headed one of the foremost research institutes in physics for three decades, and made great contributions to the advances of Chinese physics. This Festschrift in honor of Professor Yang on his centenary birthday consists of two volumes: Volume A consists of general essays concerning Professor Yang the person, as well as the authors' impressions and reminiscences of him, which are mainly (but not exclusively) in Chinese. This volume, that is Volume B, consists of over thirty scientific papers in English on subjects broadly related to his work and contributed by two different groups: Professor Yang's colleagues, friends, and former students; and graduates from the Tsinghua University Physics Department or Institute for Advanced Study, who have come under the influence of Professor Yang and are now established in their own careers; review papers presented at a Symposium held in his honor in 2021 are also included. It is hoped that this Festschrift can serve as a fit tribute to Professor Yang's lifelong achievements, and also increase public awareness of the many different sides of this giant — his life, his personality, his work, his influence, as well as what he strives for.

Non-Linear Lattice

Author: Ignazio Licata and Sauro Succi

Publisher: MDPI

Published: 2018-07-17

Total Pages: 291

ISBN-13: 3038423068

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This book is a printed edition of the Special Issue "Non-Linear Lattice" that was published in Entropy

The Universality of Physics

Author: Ramzi R. Khuri

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 199

ISBN-13: 1461505852

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Deng Feng Wang was born February 8, 1965 in Chongqing City, China and died August 15, 1999 while swimming with friends in the Atlantic Ocean off Island Beach State Park, New Jersey. In his brief life, he was to have an influence far beyond his years. On August 12th 2000, The Deng Feng Wang Memorial Conference was held at his alma mater, Princeton University, during which Deng Feng's mentors, collaborators and friends presented scientific talks in a testimonial to his tremendous influence on their work and careers. The first part of this volume contains proceedings contributions from the conference, with plenary talks by Nobel Laureate Professor Phil Anderson of Princeton University and leading Condensed Matter Theorists Professor Piers Coleman of Rutgers University and Professor Christian Gruber of the University of Lausanne. Other talks, given by collaborators, friends and classmates testify to the great breadth of Deng Feng Wang's influence, with remarkable connections shown between seemingly unrelated areas in physics such as Condensed Matter Physics, Superconductivity, One-Dimensional Models, Statistical Physics, Mathematical Physics, Quantum Field Theory, High Energy Theory, Nuclear Magnetic Resonance, Supersymmetry, M-Theory and String Theory, in addition to such varied fields outside of physics such as Oil Drilling, Mixed Signal Circuits and Neurology. The second part of the volume consists of reprints of some of Deng Feng Wang's most important papers in the areas of Condensed Matter Physics, Statistical Physics, Magnetism, Mathematical Physics and Mathematical Finance. This volume represents a fascinating synthesis of a wide variety of topics, and ultimately points to the universality of physics and of science as a whole. As such, it represents a fitting tribute to a remarkable individual, whose tragic death will never erase his enduring influence.

Classical and Quantum Nonlinear Integrable Systems

Author: A Kundu

Publisher: CRC Press

Published: 2019-04-23

Total Pages: 320

ISBN-13: 9781420034615

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Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories

Exactly Solvable Models of Strongly Correlated Electrons

Author: Vladimir E. Korepin

Publisher: World Scientific

Published: 1994

Total Pages: 506

ISBN-13: 9789810215347

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Systems of strongly correlated electrons are at the heart of recent developments in condensed matter theory. They have applications to phenomena like high-c superconductivity and the fractional quantum hall effect. Analytical solutions to such models, though mainly limited to one spatial dimension, provide a complete and unambiguous picture of the dynamics involved. This volume is devoted to such solutions obtained using the Bethe Ansatz, and concentrates on the most important of such models, the Hubbard model. The reprints are complemented by reviews at the start of each chapter and an extensive bibliography.

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.