The open XXZ chain at Δ=−1/2 and the boundary quantum Knizhnik-Zamolodchikov equations

The open XXZ spin chain with the anisotropy parameter Δ=−12 and diagonal boundary magnetic fields that depend on a parameter x is studied. For real x>0, the exact finite-size ground-state eigenvalue of the spin-chain Hamiltonian is explicitly computed. In a suitable normalisation, the ground-state components are characterised as polynomials in x with integer coefficients. Linear sum rules and special components of this eigenvector are explicitly computed in terms of determinant formulas. These results follow from the construction of a contour-integral solution to the boundary quantum Knizhnik-Zamolodchikov equations associated with the R-matrix and diagonal K-matrices of the six-vertex model. A relation between this solution and a weighted enumeration of totally-symmetric alternating sign matrices is conjectured