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

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

2007-04-26

arxiv.org/abs/0704.3542v3

Physics

Mathematical Physics

v2: cosmetic changes, new section on refined TSSCPPs vs refined ASMs

Scientific paper

10.1088/1751-8113/40/39/009

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.

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