$T$-$Q$ relation and exact solution for the XYZ chain with general nondiagonal boundary terms

Details $T$-$Q$ relation and exact solution for the XYZ chain with general nondiagonal boundary terms $T$-$Q$ relation and exact solution for the XYZ chain with general nondiagonal boundary terms

2005-12-14

arxiv.org/abs/hep-th/0512154v3

Nucl.Phys. B744 (2006) 312-329

Physics

High Energy Physics

High Energy Physics - Theory

Revtex4, 4 pages; V2, Latex file, 22 pages, the title is changed and new version contains the detailed derivations; V3, minor

Scientific paper

10.1016/j.nuclphysb.2006.03.025

We propose that the Baxter's $Q$-operator for the XYZ quantum spin chain with open boundary conditions is given by the $j\to \infty$ limit of the corresponding transfer matrix with spin-$j$ (i.e., $(2j+1)$-dimensional) auxiliary space. The associated $T$-$Q$ relation is derived from the fusion hierarchy of the model. We use this relation to determine the Bethe Ansatz solution of the eigenvalues of the fundamental transfer matrix. This solution yields the complete spectrum of the Hamiltonian.

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