The Q Q -system is an efficient method for finding complete physical solutions of Bethe Ansatz equations, but so far its application has been confined to systems possessing U(1) U ( 1 ) symmetry. We extend the rational Q Q -system framework to integrable spin chains without U(1) U ( 1 ) symmetry, exemplified by the closed XXZ model with anti-diagonal twists and the open XXZ model with non-diagonal boundary fields. We demonstrate that the Q Q -system can be derived by combining TQ T Q -relation with fusion relations of higher-spin transfer matrices. This yields QQ Q Q -relations analogous to the U(1) U ( 1 ) symmetric case but incorporating additional inhomogeneous terms. We present numerical solutions that are validated against exact diagonalization, confirming that it generates all and exclusively physical solutions.The Q Q -system is an efficient method for finding complete physical solutions of Bethe Ansatz equations, but so far its application has been confined to systems possessing U(1) U ( 1 ) symmetry. We extend the rational Q Q -system framework to integrable spin chains without U(1) U ( 1 ) symmetry, exemplified by the closed XXZ model with anti-diagonal twists and the open XXZ model with non-diagonal boundary fields. We demonstrate that the Q Q -system can be derived by combining TQ T Q -relation with fusion relations of higher-spin transfer matrices. This yields QQ Q Q -relations analogous to the U(1) U ( 1 ) symmetric case but incorporating additional inhomogeneous terms. We present numerical solutions that are validated against exact diagonalization, confirming that it generates all and exclusively physical solutions.

arXiv:2512.01551SciPost PhysicsJun 22, 20260 citations

Exact solution of the SUq (n)-invariant quantum spin chains

Hector J. de Vega, A. González-Ruiz

arXiv:hep-th/9309022Nuclear Physics BApr 1, 199490 citations

Exact surface energy of the D2(1) spin chain with generic non-diagonal boundary reflections

Guang-Liang Li, Yi Qiao, Junpeng Cao +3 more

The exact solution of the D2(1) quantum spin chain with generic non-diagonal boundary reflections is obtained. It is found that the generating functional of conserved quantities of the system can be factorized as the product of transfer matrices of two anisotropic XXZ spin chains with open boundary conditions. By using the factorization identities and the fusion technique, the eigenvalues and the Bethe ansatz equations of the model are obtained. The eigenvalues are also parameterized by the zero roots of the transfer matrix, and the patterns of root distributions are obtained. Based on them, ground states energy and the surface energies induced by the twisted boundary magnetic fields in the thermodynamic limit are obtained. These results are checked by the numerical calculations. The corresponding isotropic limit is also discussed. The results given in this paper are the foundation to study the exact physical properties of high rank Dn(1) model by using the nested processes.The exact solution of the D2(1) quantum spin chain with generic non-diagonal boundary reflections is obtained. It is found that the generating functional of conserved quantities of the system can be factorized as the product of transfer matrices of two anisotropic XXZ spin chains with open boundary conditions. By using the factorization identities and the fusion technique, the eigenvalues and the Bethe ansatz equations of the model are obtained. The eigenvalues are also parameterized by the zero roots of the transfer matrix, and the patterns of root distributions are obtained. Based on them, ground states energy and the surface energies induced by the twisted boundary magnetic fields in the thermodynamic limit are obtained. These results are checked by the numerical calculations. The corresponding isotropic limit is also discussed. The results given in this paper are the foundation to study the exact physical properties of high rank Dn(1) model by using the nested processes.

arXiv:2205.10818Nuclear Physics BAug 22, 20224 citations

The open spin-½ XXZ quantum spin chain

Chi Shi

Jan 1, 20070 citations

Rational

Q

-systems for integrable spin chains without

U(1)

symmetry