TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.4.113
TI  - Spin-$s$ rational $Q$-system
PY  - 2024/04/26
UR  - https://www.scipost.org/SciPostPhys.16.4.113
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 4
SP  - 113
A1  - Hou, Jue
AU  - Jiang, Yunfeng
AU  - Zhu, Rui-Dong
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.16.4.113,
	title={{Spin-$s$ rational $Q$-system}},
	author={Jue Hou and Yunfeng Jiang and Rui-Dong Zhu},
	journal={SciPost Phys.},
	volume={16},
	pages={113},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.4.113},
	url={https://scipost.org/10.21468/SciPostPhys.16.4.113},
}