# Spectrum of the transfer matrices of the spin chains associated with the $A^{(2)}_3$ Lie algebra

@inproceedings{Li2022SpectrumOT, title={Spectrum of the transfer matrices of the spin chains associated with the \$A^\{(2)\}\_3\$ Lie algebra}, author={Guang-Liang Li and Junpeng Cao and Xiaotian Xu and Kun Hao and Pei Sun and Tao Yang and Wen-Li Yang}, year={2022} }

We study the exact solution of quantum integrable system associated with the A (2) 3 twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the U(1) symmetry is broken. With the help of the fusion technique, we obtain the closed recursive relations of the fused transfer matrices. Based on them, together with the asymptotic behaviors and the values at special points, we obtain the eigenvalues and Bethe ansatz equations of the system. We also show that the…

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