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

Author:

Hagendorf Christian,Liénardy Jean

Abstract

Abstract The open XXZ spin chain with the anisotropy parameter Δ = 1 2 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.

Publisher

IOP Publishing

Subject

Statistics, Probability and Uncertainty,Statistics and Probability,Statistical and Nonlinear Physics

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