Overview
- Introduces basic concepts and newly developed mathematical methods of quantum integrable models
- Presents solutions of some famous long-standing problems
- Serves as both a reference work for researchers and a study text for graduate students
- Includes supplementary material: sn.pub/extras
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
About this book
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.
Reviews
In 2013, the authors made a fundamental generalization of the T-Q relation by adding an extra “inhomogeneous” term. Most notably, their new methods allow for the systematic exact solution of systems with “off-diagonal” boundaries. This book provides an excellent introduction to the new method of the off-diagonal Bethe Ansatz with applications. This monograph is destined to become a classic in the area and is highly recommended to any researcher with an interest in these topics.
---Prof. Paul A. Pearce, University of Melbourne
In 2013, the authors made a significant breakthrough in the field of quantum integrable systems. The simple - yet far reaching - solution proposed by the authors was to introduce an inhomogeneous term in the T-Q equation. The authors proceeded to demonstrate that the off-diagonal Bethe Ansatz method had general applicability, by successfully tackling numerous previously-unsolved models. This volume provides an accessible exposition of this approach, which is likely to have an enduring impact.
--- Prof. Rafael Nepomechie, University of Miami
This book provides a detailed treatment of the off-diagonal Bethe Ansatz method, with special attention given to the inhomogeneous T-Q relation pioneered recently by the authors. We find the book worthy of special attention.
---Prof. J. H. H. Perk & Prof. H. Au-Yang, Oklahoma State University
…In this book the authors outline the approach for obtaining the eigenvalue spectrum of these models in terms of their off-diagonal Bethe Ansatz method. This method overcomes the problem of not having an obvious reference state, which has long been the stumbling block for solving this class of models. The authors provide a pedagogic and extensive account, treating a number of key models. All these ingredients add up to a classic new book in a fundamentally important area of physics.
---Prof. Murray Batchelor, Chongqing University & Australian National University
Authors and Affiliations
About the authors
Prof. Yupeng Wang obtained his Ph.D in Condensed Matter Physics from Institute of Physics, Chinese Academy of Science (IOP CAS) in 1994. He joined IOP CAS as a professor in 1999, and has been the director of IOP since 2007. He is also the Vice-president of Chinese Physical Society. His research interests include Exactly solvable models in statistical mechanics and solid state physics, Quantum many-body physics, Ultra-cold atomic physics and Condensed matter theory. He has published about 150 papers in SCI indexed journals.
Prof. Wen-Li Yang obtained his Ph.D in Theoretical Physics from Northwest University of China in 1996. He was the Humboldt Foundation Research Fellow in Physikalisches Institut der Universitat Bonn during 2000-2002, Research Fellow in Kyoto University during 2002-2004, Research Associate/Fellow in University of Queensland during 2004-2009. Currently he is a professor in Northwest University in China. His main research areas are Infinite-dimensional Lie (super) algebras, (Classical) Quantum integrable systems and strongly correlated fermion systems. He has published more than 90 refereed journal articles and 8 conference papers/book chapters.
Prof. Junpeng Cao obtained his Ph.D in Theoretical Physics from Northwest University of China in 2001. He was a Postdoctoral fellow in IOP CAS during 2001-2003. He joined IOP in 2003, and was appointed as a professor of IOP in 2009. He mainly works on the field of Exactly solvable models in statistical mechanics and solid state physics. He has published 52 refereed journal articles.
Prof. Kangjie Shi obtained his Ph.D in Theoretical Physics from University of Illinois at Urbana-Champaign in 1987. He joined Northwest University of China as a professor in 1987. He mainly works on quantum (super) groups and Quantum integrable systems. He has published more than 40 refereed journal articles.
Bibliographic Information
Book Title: Off-Diagonal Bethe Ansatz for Exactly Solvable Models
Authors: Yupeng Wang, Wen-Li Yang, Junpeng Cao, Kangjie Shi
DOI: https://doi.org/10.1007/978-3-662-46756-5
Publisher: Springer Berlin, Heidelberg
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2015
Hardcover ISBN: 978-3-662-46755-8Published: 04 May 2015
Softcover ISBN: 978-3-662-51623-2Published: 18 October 2016
eBook ISBN: 978-3-662-46756-5Published: 21 April 2015
Edition Number: 1
Number of Pages: XIV, 296
Number of Illustrations: 6 b/w illustrations, 3 illustrations in colour
Topics: Mathematical Methods in Physics, Condensed Matter Physics, Quantum Field Theories, String Theory, Mathematical Physics