TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.8.3.057
TI  - Spin-$s$ $Q$-systems: Twist and open boundaries
PY  - 2025/08/27
UR  - https://www.scipost.org/SciPostPhysCore.8.3.057
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 8
IS  - 3
SP  - 057
A1  - He, Yi-Jun
AU  - Hou, Jue
AU  - Liu, Yi-Chao
AU  - Tan, Zi-Xi
AB  - In integrable spin chains, the spectral problem can be solved by the method of Bethe Ansatz, which transforms the problem of diagonalization of the Hamiltonian into the problem of solving a set of algebraic equations named Bethe equations. In this work, we systematically investigate the spin-$s$ XXX chain with twisted and open boundary conditions using the rational $Q$-system, which is a powerful tool to solve Bethe equations. We establish basic frameworks of the rational $Q$-system and confirm its completeness numerically in both cases. For twisted boundaries, we investigate the polynomiality conditions of the rational $Q$-system and derive physical conditions for singular solutions of Bethe equations. For open boundaries, we uncover novel phenomena such as hidden symmetries and boundary induced strings under specific boundary parameters. Hidden symmetries lead to the appearance of extra degeneracies in the Hilbert space, while the boundary induced string is a novel type of exact string configuration, whose length depends on the boundary magnetic fields. These findings, supported by both analytical and numerical evidences, offer new insights into the interplay between symmetries and boundary conditions.
ER  -

@Article{10.21468/SciPostPhysCore.8.3.057,
	title={{Spin-$s$ $Q$-systems: Twist and open boundaries}},
	author={Yi-Jun He and Jue Hou and Yi-Chao Liu and Zi-Xi Tan},
	journal={SciPost Phys. Core},
	volume={8},
	pages={057},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.8.3.057},
	url={https://scipost.org/10.21468/SciPostPhysCore.8.3.057},
}