SciPost logo

Spin-$s$ rational $Q$-system

Jue Hou, Yunfeng Jiang, Rui-Dong Zhu

SciPost Phys. 16, 113 (2024) · published 26 April 2024


Bethe Ansatz equations for spin-s Heisenberg spin chain with s≥1 are significantly more difficult to analyze than the spin-$\tfrac{1}{2}$ case, due to the presence of repeated roots. As a result, it is challenging to derive extra conditions for the Bethe roots to be physical and study the related completeness problem. In this paper, we propose the rational Q-system for the XXX$_s$ spin chain. Solutions of the proposed Q-system give all and only physical solutions of the Bethe Ansatz equations required by completeness. This is checked numerically and proved rigorously. The rational Q-system is equivalent to the requirement that the solution and the corresponding dual solution of the TQ-relation are both polynomials, which we prove rigorously. Based on this analysis, we propose the extra conditions for solutions of the XXX$_s$ Bethe Ansatz equations to be physical.

Cited by 2

Crossref Cited-by

Authors / Affiliations: mappings to Contributors and Organizations

See all Organizations.
Funders for the research work leading to this publication