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.

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

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

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