The open XXZ chain at $\Delta =-1/2$ and totally-symmetric alternating sign matrices

Abstract

The open XXZ spin chain with the anisotropy parameter $\Delta =-\frac{1}{2}$, diagonal boundary fields that depend on a parameter $x$, and finite length $N$ is studied. In a natural normalisation, the components of its ground-state vector are polynomials in $x$ with integer coefficients. It is shown that their sum is given by a generating function for the weighted enumeration of totally-symmetric alternating sign matrices with weights depending on $x$.

arXiv comment32 pages, 4 figures; V2: refinements to the proof of Theorem 4.1; correction of a referencing issue