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arXiv · 2509.09209

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

Jean Liénardy·Christian Walmsley Hagendorf
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Abstract

The open XXZ spin chain with the anisotropy parameter $\Delta=-\frac12$, 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 $x$.

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Jean Liénardy, Christian Walmsley Hagendorf. 2025-09-11. The open XXZ chain at $\Delta=-1/2$ and totally-symmetric alternating sign matrices. https://arxiv.org/abs/2509.09209

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