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

The open XXZ spin chain with the anisotropy parameter $\Delta=-\frac12$ and diagonal boundary magnetic fields that depend on a $x$ is studied. For real $x>0$, exact finite-size ground-state eigenvalue of spin-chain Hamiltonian explicitly computed. In suitable normalisation, components are characterised as polynomials in integer coefficients. Linear sum rules special this eigenvector computed terms determinant formulas. These results follow from construction contour-integral solution to quantum Knizhnik-Zamolodchikov equations associated $R$-matrix $K$-matrices six-vertex model. A relation between weighted enumeration totally-symmetric alternating sign matrices conjectured.