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Off-Diagonal Bethe Ansatz for Exactly Solvable Models
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This book introduces the off-diagonal Bethe ansatz method, an unified analytic theory for the eigenvalue problem of quantum integrable models. Based on the intrinsic properties of the R-matrix and the K-matrices, a systematic method to construct the operator identities of the transfer matrix is introduced. Those identities allow one to establish the inhomogeneous T-Q relation formalism and the Bethe ansatz equations. The advantage of this method is that it overcomes the obstacle of the reference state. Several longstanding models, which had never been solved via other methods, can be solved via this method. Both the exact results and the off-diagonal Bethe ansatz method itself have important applications in quantum field theory, low-dimensional condensed matter physics, statistical physics and cold atom systems.
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