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 Physics A Mathematical and Theoretical

Exact solution of the B 1 model

Panpan Xue, Guang-Liang Li, Junpeng Cao, Kun Hao, Wen‐Li Yang, Kangjie Shi

Published Feb 22, 2019• 1 citation
Publisher

Abstract

Abstract The B 1 vertex model is studied by the off-diagonal Bethe ansatz method. New closed operator product identities of the fused transfer matrices are obtained by using the fusion technique. Based on them and the asymptotic behaviors as well as the values of the fused transfer matrices at certain points, the exact solutions of the B 1 model with periodic and with integrable off-diagonal open boundary conditions are obtained. We find that the degree of the polynomial of the inhomogeneous T − Q relation is lower. The B 1 model is equivalent to the integrable spin-1 Heisenberg chain, thus the method and the results in this paper can be generalized to the high spin Heisenberg model and the integrable models associated with B n Lie algebra.

DOI
10.1088/1751-8121/ab09ac

Related papers

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

Exact solution of a quantum integrable system associated with the G2 exceptional Lie algebra

Guang-Liang Li, Junpeng Cao, Pei Sun +3 more

A quantum integrable spin chain model associated with the G 2 exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to derive the exact energy spectrum and Bethe ansatz equations of the system based on polynomial analysis. The present method provides a unified treatment to investigate the Bethe ansatz solutions for both the periodic and the non-diagonal open boundary conditions associated with exceptional Lie algebras.

arXiv:2408.04201•Nuclear Physics B•Dec 13, 2024•3 citations

Off-diagonal Bethe Ansatz for the $$ {D}_3^{(1)} $$ model

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

Abstract The exact solutions of the $$ {D}_3^{(1)} $$ D 3 1 model (or the so(6) quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator product identities are obtained, which are sufficient to enable us to determine spectrum of the system. Eigenvalues of the fused transfer matrices are constructed by the T - Q relations for the periodic case and by the inhomogeneous T- Q one for the non-diagonal boundary reflection case. The present method can be generalized to deal with the $$ {D}_n^{(1)} $$ D n 1 model directly.

arXiv:1909.08534•Journal of High Energy Physics•Dec 1, 2019•5 citations

Graded off-diagonal Bethe ansatz solution of the SU(2|2) spin chain model with generic integrable boundaries

Xiaotian Xu, Junpeng Cao, Yi Qiao +3 more

The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the SU(2|2) vertex model with both periodic and generic open boundary conditions are constructed. By generalizing the fusion techniques to the supersymmetric case, a closed set of operator product identities about the transfer matrices are derived, which allows us to give the eigenvalues in terms of homogeneous or inhomogeneous T−Q relations. The method and results provided in this paper can be generalized to other high rank supersymmetric quantum integrable models.

arXiv:2007.10666•Nuclear Physics B•Oct 1, 2020•0 citations
Abstract The B 1 vertex model is studied by the off-diagonal Bethe ansatz method. New closed operator product identities of the fused transfer matrices are obtained by using the fusion technique. Based on them and the asymptotic behaviors as well as the values of the fused transfer matrices at certain points, the exact solutions of the B 1 model with periodic and with integrable off-diagonal open boundary conditions are obtained. We find that the degree of the polynomial of the inhomogeneous T − Q relation is lower. The B 1 model is equivalent to the integrable spin-1 Heisenberg chain, thus the method and the results in this paper can be generalized to the high spin Heisenberg model and the integrable models associated with B n Lie 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.
A quantum integrable spin chain model associated with the G 2 exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to derive the exact energy spectrum and Bethe ansatz equations of the system based on polynomial analysis. The present method provides a unified treatment to investigate the Bethe ansatz solutions for both the periodic and the non-diagonal open boundary conditions associated with exceptional Lie algebras.
Off-diagonal Bethe Ansatz for the D3(1) {D}_3^{(1)} D3(1)​ model
Abstract The exact solutions of the D3(1) {D}_3^{(1)} D3(1)​ D 3 1 model (or the so(6) quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator product identities are obtained, which are sufficient to enable us to determine spectrum of the system. Eigenvalues of the fused transfer matrices are constructed by the T - Q relations for the periodic case and by the inhomogeneous T- Q one for the non-diagonal boundary reflection case. The present method can be generalized to deal with the Dn(1) {D}_n^{(1)} Dn(1)​ D n 1 model directly.
The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the SU(2|2) vertex model with both periodic and generic open boundary conditions are constructed. By generalizing the fusion techniques to the supersymmetric case, a closed set of operator product identities about the transfer matrices are derived, which allows us to give the eigenvalues in terms of homogeneous or inhomogeneous T−Q relations. The method and results provided in this paper can be generalized to other high rank supersymmetric quantum integrable models.