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9783662467558

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In 2013, the authors made a significant breakthrough in the field of quantum integrable systems. Indeed, recall that a key feature of the periodic Heisenberg quantum spin chain is that the spectrum (eigenvalues T of the transfer matrix) can be characterized by the zeros ( Bethe roots ) of a polynomial ( Q-function ) that satisfies a homogeneous second order finite difference equation ( Baxter TQ equation ). Similar relations hold for the other quantum integrable models that had been solved until that time. However, there remained a number of interesting integrable models (such as the open Heisenberg quantum spin chain with generic boundary fields) that had resisted solution. The obstacle was that three basic requirements (polynomial Q-function, asymptotic behavior of T, and T-Q equation) could not be simultaneously satisfied. The simple - yet far reaching - solution proposed by the authors was to introduce an inhomogeneous term in the T-Q equation. The authors then proceeded to demonstrate that this approach (which they dubbed off diagonal Bethe Ansatz ) 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.

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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.

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