TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.5.129
TI  - Rational Q-systems at root of unity I. Closed chains
PY  - 2024/05/22
UR  - https://scipost.org/SciPostPhys.16.5.129
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 5
SP  - 129
A1  - Hou, Jue
AU  - Jiang, Yunfeng
AU  - Miao, Yuan
AB  - The solution of Bethe Ansatz equations for XXZ spin chain with the parameter q being a root of unity is infamously subtle. In this work, we develop the rational Q-system for this case, which offers a systematic way to find all physical solutions of the Bethe Ansatz equations at root of unity. The construction contains two parts. In the first part, we impose additional constraints to the rational Q-system. These constraints eliminate the so-called Fabricius-McCoy (FM) string solutions, yielding all primitive solutions. In the second part, we give a simple procedure to construct the descendant tower of any given primitive state. The primitive solutions together with their descendant towers constitute the complete Hilbert space. We test our proposal by extensive numerical checks and apply it to compute the torus partition function of the 6-vertex model at root of unity.
ER  -

@Article{10.21468/SciPostPhys.16.5.129,
	title={{Rational Q-systems at root of unity I. Closed chains}},
	author={Jue Hou and Yunfeng Jiang and Yuan Miao},
	journal={SciPost Phys.},
	volume={16},
	pages={129},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.5.129},
	url={https://scipost.org/10.21468/SciPostPhys.16.5.129},
}