Off-Diagonal Bethe Ansatz for Exactly Solvable Models

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.

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

Autorentext

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.

Inhalt
Overview.- The algebraic Bethe ansatz.- The periodic anisotropic spin-1/2 chains.- The spin-1/2 torus.- The spin-1/2 chain with arbitrary boundary fields.- The one-dimensional Hubbard model.- The nested off-diagonal Bethe ansatz.- The hierarchical off-diagonal Bethe Ansatz.- The Izergin-Korepin model.