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 General

Integrable model of interacting XY chains

R. Z. Bariev

Published Aug 21, 1991• 44 citations
Publisher

Abstract

An exact diagonalization of the Hamiltonian for the one-dimensional quantum model consisting of an arbitrary number of isotropic XY chains connected by many-spin interactions is carried out with the help of the generalized nested Bethe ansatz. An exact solution for the ground-state energy of the considered model is obtained.
DOI
10.1088/0305-4470/24/16/007

Related papers

Integrable spin chain with two- and three-particle interactions

R. Z. Bariev

The one-dimensional model which consists of two isotropic XY chains with spins S=1/2 coupled by three-spin interactions is considered with the help of the Bethe ansatz. It is shown that the diagonalization of the Hamiltonian can be reduced to solving a set of coupled nonlinear equations. The exact solution of these equations corresponding to the ground state of system is obtained. The model considered exhibits a ground state of Anderson type with the finite magnetization along the quantization axis.

Advanced series in mathematical physics•May 1, 1994•0 citations

Integrable spin chain with two- and three-particle interactions

R. Z. Bariev

The one-dimensional model which consists of two isotropic XY chains with spins S=1/2 coupled by three-spin interactions is considered with the help of the Bethe ansatz. It is shown that the diagonalization of the Hamiltonian can be reduced to solving a set of coupled nonlinear equations. The exact solution of these equations corresponding to the ground state of system is obtained. The model considered exhibits a ground state of Anderson type with the finite magnetization along the quantization axis.

Journal of Physics A Mathematical and General•May 21, 1991•92 citations

Exact solution of an integrable quantum spin chain with competing interactions*

Jian Wang, Yi Qiao, Junpeng Cao +1 more

We construct an integrable quantum spin chain that includes the nearest-neighbor, next-nearest-neighbor, chiral three-spin couplings, Dzyloshinsky–Moriya interactions and unparallel boundary magnetic fields. Although the interactions in bulk materials are isotropic, the spins nearby the boundary fields are polarized, which induce the anisotropic exchanging interactions of the first and last bonds. The U(1) symmetry of the system is broken because of the off-diagonal boundary reflections. Using the off-diagonal Bethe ansatz, we obtain an exact solution to the system. The inhomogeneous T–Q relation and Bethe ansatz equations are given explicitly. We also calculate the ground state energy. The method given in this paper provides a general way to construct new integrable models with certain interesting interactions.

Chinese Physics B•Apr 22, 2021•1 citation

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

On the Quantum Integrability for A Model of Coupled XY Chains

Huan-Qiang Zhou, Xiangyu Ge

The paper discusses integrable open-boundary conditions for the model of three coupled one-dimensional XY spin chains in the framework of the quantum inverse scattering method. The diagonal boundary K-matrices are found and a class of integrable boundary terms are determined. The boundary model Hamiltonian is solved by using the coordinate space Bethe ansatz technique and Bathe ansatz equations are derived.

•Jan 1, 1999•0 citations

Exact solution of the $SU_{q}(n)$ invariant quantum spin chains

Hector J. de Vega, González-Ruiz, A

The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the $A_{n-1}$ vertex model with fixed open boundary conditions and the corresponding $SU_{q}(n)$ invariant hamiltonian. The Bethe Ansatz equations obtained are solved in the thermodynamic limit giving the vertex model free energy and the hamiltonian ground state energy including the corresponding boundary contributions.

•Sep 3, 1993•80 citations
The one-dimensional model which consists of two isotropic XY chains with spins S=1/2 coupled by three-spin interactions is considered with the help of the Bethe ansatz. It is shown that the diagonalization of the Hamiltonian can be reduced to solving a set of coupled nonlinear equations. The exact solution of these equations corresponding to the ground state of system is obtained. The model considered exhibits a ground state of Anderson type with the finite magnetization along the quantization axis.
The one-dimensional model which consists of two isotropic XY chains with spins S=1/2 coupled by three-spin interactions is considered with the help of the Bethe ansatz. It is shown that the diagonalization of the Hamiltonian can be reduced to solving a set of coupled nonlinear equations. The exact solution of these equations corresponding to the ground state of system is obtained. The model considered exhibits a ground state of Anderson type with the finite magnetization along the quantization axis.
We construct an integrable quantum spin chain that includes the nearest-neighbor, next-nearest-neighbor, chiral three-spin couplings, Dzyloshinsky–Moriya interactions and unparallel boundary magnetic fields. Although the interactions in bulk materials are isotropic, the spins nearby the boundary fields are polarized, which induce the anisotropic exchanging interactions of the first and last bonds. The U(1) symmetry of the system is broken because of the off-diagonal boundary reflections. Using the off-diagonal Bethe ansatz, we obtain an exact solution to the system. The inhomogeneous T–Q relation and Bethe ansatz equations are given explicitly. We also calculate the ground state energy. The method given in this paper provides a general way to construct new integrable models with certain interesting interactions.
Exact solution of the SUq(n)SU_{q}(n)SUq​(n) invariant quantum spin chains
The Nested Bethe Ansatz is generalized to open boundary conditions. This is used to find the exact eigenvectors and eigenvalues of the An−1A_{n-1}An−1​ vertex model with fixed open boundary conditions and the corresponding SUq(n)SU_{q}(n)SUq​(n) invariant hamiltonian. The Bethe Ansatz equations obtained are solved in the thermodynamic limit giving the vertex model free energy and the hamiltonian ground state energy including the corresponding boundary contributions.