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

arXiv:2205.10818 · Nuclear Physics B

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

Guang-Liang Li, Yi Qiao, Junpeng Cao, Wen‐Li Yang, Kangjie Shi, Yupeng Wang

Published Aug 22, 2022• 4 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1016/j.nuclphysb.2022.115946

Related papers

Exact physical quantities of the $$ {D}_2^{(2)} $$ spin chain model with generic open boundary conditions

Pengcheng Lu, Junpeng Cao, Wen‐Li Yang +2 more

A bstract We study the quantum integrable spin chain model associated with the twisted $$ {D}_2^{(2)} $$ D 2 2 algebra (or simply the $$ {D}_2^{(2)} $$ D 2 2 model) under generic open boundary conditions. The Hamiltonian of this model can be factorized into the sum of two staggered XXZ spin chains. Applying the t - W method, we derive the homogeneous Bethe ansatz equations for the zeros of the transfer matrix eigenvalues and the patterns of the corresponding zeros of the staggered XXZ spin chain with generic integrable boundaries. Based on these results, we analytically compute the surface energies and excitation energies of the $$ {D}_2^{(2)} $$ D 2 2 model in different regimes of boundary parameters.

arXiv:2502.09262•Journal of High Energy Physics•May 15, 2025•1 citation

Root patterns and exact surface energy of the spin-1 Heisenberg model with generic open boundaries

Jiasheng Dong, Pengcheng Lu, Junpeng Cao +3 more

Abstract We investigate the thermodynamic limit and exact surface energy of the isotropic spin-1 Heisenberg chain with integrable generic open boundary conditions by a novel Bethe ansatz method. We obtain the homogeneous (or two-term) Bethe ansatz like equations for the zero roots of the transfer matrix. Based on the patterns of the zero roots, we analytical calculate the densities of zero roots and the surface energies of the model in all regimes of the boundary parameters.

arXiv:2401.03172•Journal of Physics A Mathematical and Theoretical•Jul 3, 2024•2 citations

Spectrum of the quantum integrable $$ {D}_2^{(2)} $$ spin chain with generic boundary fields

Guang-Liang Li, Junpeng Cao, Wen‐Li Yang +2 more

Abstract Exact solution of the quantum integrable $$ {D}_2^{(2)} $$ D 2 2 spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered anisotropic XXZ spin chains. Based on this identity, the eigenvalues and Bethe ansatz equations of the $$ {D}_2^{(2)} $$ D 2 2 model are derived via off-diagonal Bethe ansatz.

arXiv:2202.06531•Journal of High Energy Physics•Apr 19, 2022•6 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

Surface energy and elementary excitations of the XYZ spin chain with integrable open boundary fields

Zhirong Xin, Junpeng Cao, Wen‐Li Yang +1 more

A bstract We study the thermodynamic limit of the anisotropic XYZ spin chain with non-diagonal integrable open boundary conditions. Although the U(1)-symmetry is broken, by using the new parametrization scheme, we exactly obtain the surface energy and the excitation energy of the system, which has solved the difficulty in the inhomogeneous T − Q relation. With the boundary parameters in the regions making the Hamiltonian Hermitian, we have obtained the distribution patterns of the zeros of the eigenvalue of the transfer matrix for the ground state and the excited ones. We find that the surface and excitation energies depend on the parities of sites number N , due to the long-range Neel order in the bulk. The easy-axis and thermodynamic limit for all the regions of boundary parameters are studied. We also obtain the physical quantities in the thermodynamic limit of boundary XXZ model by taking the trigonometric limit.

arXiv:2404.19240•Journal of High Energy Physics•Oct 10, 2024•2 citations

Exact physical quantities of the XYZ spin chain in the thermodynamic limit

Zhirong Xin, Junpeng Cao, Wen‐Li Yang +1 more

A bstract The thermodynamic limits of the XYZ spin chain with periodic or twisted boundary conditions are studied. By using the technique of characterizing the eigenvalue of the transfer matrix by the T − Q relation and by the zeros of the associated polynomial, we obtain the constraints of the Bethe roots and the zeros for the eigenvalues. With the help of structure of Bethe roots, we obtain the distribution patterns of zeros. Based on them, the physical quantities such as the surface energy and excitation energy are calculated. We find that both of them depend on the parity of sites number due to the topological long-range Neel order on the Mobius manifold in the spin space. We also check our results with those obtaining by the density matrix renormalization group. The method provided in this paper can be applied to study the thermodynamic properties at the thermal equilibrium state with finite temperature.

arXiv:2411.12200•Journal of High Energy Physics•Feb 13, 2025•0 citations
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.
Exact physical quantities of the D2(2) {D}_2^{(2)} D2(2)​ spin chain model with generic open boundary conditions
A bstract We study the quantum integrable spin chain model associated with the twisted D2(2) {D}_2^{(2)} D2(2)​ D 2 2 algebra (or simply the D2(2) {D}_2^{(2)} D2(2)​ D 2 2 model) under generic open boundary conditions. The Hamiltonian of this model can be factorized into the sum of two staggered XXZ spin chains. Applying the t - W method, we derive the homogeneous Bethe ansatz equations for the zeros of the transfer matrix eigenvalues and the patterns of the corresponding zeros of the staggered XXZ spin chain with generic integrable boundaries. Based on these results, we analytically compute the surface energies and excitation energies of the D2(2) {D}_2^{(2)} D2(2)​ D 2 2 model in different regimes of boundary parameters.
Spectrum of the quantum integrable D2(2) {D}_2^{(2)} D2(2)​ spin chain with generic boundary fields
Abstract Exact solution of the quantum integrable D2(2) {D}_2^{(2)} D2(2)​ D 2 2 spin chain with generic integrable boundary fields is constructed. It is found that the transfer matrix of this model can be factorized as the product of those of two open staggered anisotropic XXZ spin chains. Based on this identity, the eigenvalues and Bethe ansatz equations of the D2(2) {D}_2^{(2)} D2(2)​ D 2 2 model are derived via off-diagonal Bethe ansatz.
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.
A bstract We study the thermodynamic limit of the anisotropic XYZ spin chain with non-diagonal integrable open boundary conditions. Although the U(1)-symmetry is broken, by using the new parametrization scheme, we exactly obtain the surface energy and the excitation energy of the system, which has solved the difficulty in the inhomogeneous T − Q relation. With the boundary parameters in the regions making the Hamiltonian Hermitian, we have obtained the distribution patterns of the zeros of the eigenvalue of the transfer matrix for the ground state and the excited ones. We find that the surface and excitation energies depend on the parities of sites number N , due to the long-range Neel order in the bulk. The easy-axis and thermodynamic limit for all the regions of boundary parameters are studied. We also obtain the physical quantities in the thermodynamic limit of boundary XXZ model by taking the trigonometric limit.
A bstract The thermodynamic limits of the XYZ spin chain with periodic or twisted boundary conditions are studied. By using the technique of characterizing the eigenvalue of the transfer matrix by the T − Q relation and by the zeros of the associated polynomial, we obtain the constraints of the Bethe roots and the zeros for the eigenvalues. With the help of structure of Bethe roots, we obtain the distribution patterns of zeros. Based on them, the physical quantities such as the surface energy and excitation energy are calculated. We find that both of them depend on the parity of sites number due to the topological long-range Neel order on the Mobius manifold in the spin space. We also check our results with those obtaining by the density matrix renormalization group. The method provided in this paper can be applied to study the thermodynamic properties at the thermal equilibrium state with finite temperature.