Polynomial solutions of qKZ equation and ground state of XXZ spin chain at Delta = -1/2

Abstract

Integral formulae for polynomial solutions of the quantum Knizhnik-Zamolodchikov equations associated with the R-matrix of the six-vertex model are considered. It is proved that when the deformation parameter q is equal to e^{+- 2 pi i/3} and the number of vertical lines of the lattice is odd, the solution under consideration is an eigenvector of the inhomogeneous transfer matrix of the six-vertex model. In the homogeneous limit it is a ground state eigenvector of the antiferromagnetic XXZ spin chain with the anisotropy parameter Delta equal to -1/2 and odd number of sites. The obtained integral representations for the components of this eigenvector allow to prove some conjectures on its properties formulated earlier. A new statement relating the ground state components of XXZ spin chains and Temperley-Lieb loop models is formulated and proved.

arXiv commentv2: cosmetic changes, new section on refined TSSCPPs vs refined ASMs

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Cited by in corpus (20)

• Matrix product formula for Macdonald polynomials
• Spin chains with dynamical lattice supersymmetry
• A possible combinatorial point for XYZ-spin chain
• Open spin chains with dynamic lattice supersymmetry
• Multiply-refined enumeration of alternating sign matrices
• Jack polynomial fractional quantum Hall states and their generalizations
• Extended Joseph polynomials, quantized conformal blocks, and a q-Selberg type integral
• Finite size emptiness formation probability of the XXZ spin chain at $\Delta =-1/2$
• Spin-Ruijsenaars, q-deformed Haldane-Shastry and Macdonald polynomials
• Boundary transfer matrices and boundary quantum KZ equations
• The nineteen-vertex model and alternating sign matrices
• On some ground state components of the O(1) loop model
• On the transfer matrix of the supersymmetric eight-vertex model. I. Periodic boundary conditions
• Boundary emptiness formation probabilities in the six-vertex model at $\Delta =-\frac{1}{2}$
• Symmetry classes of alternating sign matrices in the nineteen-vertex model
• Sum rules for the supersymmetric eight-vertex model
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder
• On Baxter's Q operator of the higher spin XXZ chain at the Razumov-Stroganov point
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations
• Exact densities of loops in O(1) dense loop model and of clusters in critical percolation on a cylinder II: rotated lattice