The open XXZ chain at Δ=−1/2 and the boundary quantum Knizhnik-Zamolodchikov equations
(2021) Journal of Statistical Mechanics: Theory and Experiment —
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- Abstract
- 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.
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Walmsley Hagendorf, C., & Liénardy, J. (2021). The open XXZ chain at Δ=−1/2 and the boundary quantum Knizhnik-Zamolodchikov equations. Journal of Statistical Mechanics: Theory and Experiment. https://doi.org/10.1088/1742-5468/abd028