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arXiv · 2008.03220

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

Christian Hagendorf·Jean Liénardy
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Abstract

The open XXZ spin chain with the anisotropy parameter $Δ=-\frac12$ 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.

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Christian Hagendorf, Jean Liénardy. 2022-03-25. The open XXZ chain at $Δ=-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations. https://doi.org/10.1088/1742-5468%2Fabd028

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