Generalized T-Q relations and the open XXZ chain

Abstract

We propose a generalization of the Baxter T-Q relation which involves more than one independent Q(u). We argue that the eigenvalues of the transfer matrix of the open XXZ quantum spin chain are given by such generalized T-Q relations, for the case that at most two of the boundary parameters {α_-, α_+, β_-, β_+} are nonzero, and the bulk anisotropy parameter has values η= i π/2, iπ/4, ...

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• Bethe ansatz for the XXX-S chain with non-diagonal open boundaries
• Solution of the SU(N) Vertex Model with Non-Diagonal Open Boundaries
• Exact solution of the $A_{n-1}^{(1)}$ trigonometric vertex model with non-diagonal open boundaries

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• Boundary energy of the general open XXZ chain at roots of unity
• All product eigenstates in Heisenberg models from a graphical construction
• Nested algebraic Bethe ansatz for open GL(N) spin chains with projected K-matrices
• Bethe Ansatz and boundary energy of the open spin-1/2 XXZ chain