Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Mathematical Physics

An anisotropic four-component spin chain with integrable boundary terms

Panpan Xue, Guang-Liang Li, Junpeng Cao, Jiao Li, Kun Hao, Tao Yang, Wen‐Li Yang

Published Apr 1, 2019• 0 citations
Publisher

Abstract

The anisotropic four-component spin chain with integrable off-diagonal boundary terms is studied by the nested off-diagonal Bethe ansatz method. Based on the intrinsic properties of the associated R-matrix, the recursive operator product identities of the fused transfer matrices are obtained by using the fusion. The asymptotic behaviors and the values of fused transfer matrices at certain special points are derived explicitly. The nested inhomogeneous T − Q relations of the system are constructed, and the self-consistency of these relations is demonstrated. The method and the results can be applied to study the eigenvalue problems of multicomponent integrable models with open boundaries.

DOI
10.1063/1.5086721

Related papers

Nested off-diagonal Bethe ansatz and exact solutions of the su(n) spin chain with generic integrable boundaries

Junpeng Cao, Wen‐Li Yang, Kangjie Shi +1 more

The nested off-diagonal Bethe ansatz method is proposed to diagonalize multi-component integrable models with generic integrable boundaries. As an example, the exact solutions of the su(n)-invariant spin chain model with both periodic and non-diagonal boundaries are derived by constructing the nested T − Q relations based on the operator product identities among the fused transfer matrices and the asymptotic behavior of the transfer matrices.

arXiv:1312.4770•Journal of High Energy Physics•Apr 1, 2014•37 citations

Exact solution of the trigonometric SU(3) spin chain with generic off-diagonal boundary reflections

Guang-Liang Li, Junpeng Cao, Kun Hao +3 more

The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the SUq(3) R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T–Q relations and Bethe ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the SUq(n) algebra.

arXiv:1602.02042•Nuclear Physics B•Jul 16, 2016•2 citations

Exact solution of the XXZ alternating spin chain with generic non-diagonal boundaries

Cao, Junpeng, Wen‐Li Yang, Kangjie Shi +1 more

The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused R-matrices and K-matrices, we obtain certain closed operator identities and conditions, which allow us to construct an inhomogeneous T-Q relation and the associated Bethe Ansatz equations accounting for the eigenvalues of the transfer matrix.

arXiv:1409.3646•Sep 12, 2014•5 citations

Exact solutions of the C quantum spin chain

Guang-Liang Li, Panpan Xue, Pei Sun +5 more

We study the exact solutions of quantum integrable model associated with the Cn Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method. Taking the C3 as an example we demonstrate how the generalized method works. We give the fusion structures of the model and provide a way to close fusion processes. Based on the resulted operator product identities among fused transfer matrices and some necessary additional constraints such as asymptotic behaviors and relations at some special points, we obtain the eigenvalues of transfer matrices and parameterize them as homogeneous T−Q relations in the periodic case or inhomogeneous ones in the open case. We also give the exact solutions of the Cn model with an off-diagonal open boundary condition. The method and results in this paper can be generalized to other high rank integrable models associated with other Lie algebras.

arXiv:2011.02746•Nuclear Physics B•Feb 5, 2021•5 citations

Exact solution of the quantum integrable model associated with the twisted $$ {\mathrm{D}}_3^{(2)} $$ algebra

Guang-Liang Li, Xiaotian Xu, Kun Hao +5 more

Abstract We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $$ {D}_3^{(2)} $$ D 3 2 algebra (or the $$ {D}_3^{(2)} $$ D 3 2 model) with either periodic or integrable open boundary conditions. We obtain the intrinsic operator product identities among the fused transfer matrices and find a way to close the recursive fusion relations, which makes it possible to determinate eigenvalues of transfer matrices with an arbitrary anisotropic parameter η. Based on them, and the asymptotic behaviors and values at certain points, we construct eigenvalues of transfer matrices in terms of homogeneous T − Q relations for the periodic case and inhomogeneous ones for the open case with some off-diagonal boundary reflections. The associated Bethe ansatz equations are also given. The method and results in this paper can be generalized to the $$ {D}_{n+1}^{(2)} $$ D n + 1 2 model and other high rank integrable models.

arXiv:2110.02699•Journal of High Energy Physics•Mar 1, 2022•3 citations

Exact solution of the sp(4) integrable spin chain with generic boundaries

Guang-Liang Li, Junpeng Cao, Panpan Xue +5 more

Abstract The off-diagonal Bethe ansatz method is generalized to the integrable model associated with thesp(4) (orC2) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer matrices. These relations, together with some asymptotic behaviors and values of the transfer matrices at certain points, enable us to determine the eigenvalues of the transfer matrices completely. For the periodic boundary condition case, we recover the sameT−Qrelations obtained via conventional Bethe ansatz methods previously, while for the off-diagonal boundary condition case, the eigenvalues are given in terms of inhomogeneousT−Qrelations, which could not be obtained by the conventional Bethe ansatz methods. The method developed in this paper can be directly generalized to genericsp(2n) (i.e.,Cn) integrable model.

arXiv:1812.03618•Journal of High Energy Physics•May 1, 2019•6 citations
The anisotropic four-component spin chain with integrable off-diagonal boundary terms is studied by the nested off-diagonal Bethe ansatz method. Based on the intrinsic properties of the associated R-matrix, the recursive operator product identities of the fused transfer matrices are obtained by using the fusion. The asymptotic behaviors and the values of fused transfer matrices at certain special points are derived explicitly. The nested inhomogeneous T − Q relations of the system are constructed, and the self-consistency of these relations is demonstrated. The method and the results can be applied to study the eigenvalue problems of multicomponent integrable models with open boundaries.
The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the SUq(3) R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator identities among the fused transfer matrices at the inhomogeneous points are derived. The corresponding asymptotic behaviors of the transfer matrices and their values at some special points are given in detail. Based on the functional analysis, a nested inhomogeneous T–Q relations and Bethe ansatz equations of the system are obtained. These results can be naturally generalized to cases related to the SUq(n) algebra.
We study the exact solutions of quantum integrable model associated with the Cn Lie algebra, with either a periodic or an open one with off-diagonal boundary reflections, by generalizing the nested off-diagonal Bethe ansatz method. Taking the C3 as an example we demonstrate how the generalized method works. We give the fusion structures of the model and provide a way to close fusion processes. Based on the resulted operator product identities among fused transfer matrices and some necessary additional constraints such as asymptotic behaviors and relations at some special points, we obtain the eigenvalues of transfer matrices and parameterize them as homogeneous T−Q relations in the periodic case or inhomogeneous ones in the open case. We also give the exact solutions of the Cn model with an off-diagonal open boundary condition. The method and results in this paper can be generalized to other high rank integrable models associated with other Lie algebras.
Exact solution of the quantum integrable model associated with the twisted D3(2) {\mathrm{D}}_3^{(2)} D3(2)​ algebra
Abstract We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted D3(2) {D}_3^{(2)} D3(2)​ D 3 2 algebra (or the D3(2) {D}_3^{(2)} D3(2)​ D 3 2 model) with either periodic or integrable open boundary conditions. We obtain the intrinsic operator product identities among the fused transfer matrices and find a way to close the recursive fusion relations, which makes it possible to determinate eigenvalues of transfer matrices with an arbitrary anisotropic parameter η. Based on them, and the asymptotic behaviors and values at certain points, we construct eigenvalues of transfer matrices in terms of homogeneous T − Q relations for the periodic case and inhomogeneous ones for the open case with some off-diagonal boundary reflections. The associated Bethe ansatz equations are also given. The method and results in this paper can be generalized to the Dn+1(2) {D}_{n+1}^{(2)} Dn+1(2)​ D n + 1 2 model and other high rank integrable models.
Abstract The off-diagonal Bethe ansatz method is generalized to the integrable model associated with thesp(4) (orC2) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer matrices. These relations, together with some asymptotic behaviors and values of the transfer matrices at certain points, enable us to determine the eigenvalues of the transfer matrices completely. For the periodic boundary condition case, we recover the sameT−Qrelations obtained via conventional Bethe ansatz methods previously, while for the off-diagonal boundary condition case, the eigenvalues are given in terms of inhomogeneousT−Qrelations, which could not be obtained by the conventional Bethe ansatz methods. The method developed in this paper can be directly generalized to genericsp(2n) (i.e.,Cn) integrable model.