arXiv:2502.09262 · Journal of High Energy Physics

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

Pengcheng Lu, Junpeng Cao, Wen‐Li Yang, Ian Marquette, Yao-Zhong Zhang

Published May 15, 2025• 1 citation

Abstract

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.

DOI: 10.1007/jhep05(2025)137

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arXiv:2502.09262 · Journal of High Energy Physics

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

Pengcheng Lu, Junpeng Cao, Wen‐Li Yang, Ian Marquette, Yao-Zhong Zhang

Published May 15, 2025• 1 citation

arXiv HTML PDF

Abstract

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.

DOI: 10.1007/jhep05(2025)137

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Abstract We express ${D}_2^{(2)}$ D 2 2 transfer matrices as products of ${A}_1^{(1)}$ A 1 1 transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz. We also formulate and solve a new integrable XXZ-like open spin chain with an even number of sites that depends on a continuous parameter, which we interpret as the rapidity of the boundary.Abstract We express $$ {D}_2^{(2)} $$ D 2 2 transfer matrices as products of $$ {A}_1^{(1)} $$ A 1 1 transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz. We also formulate and solve a new integrable XXZ-like open spin chain with an even number of sites that depends on a continuous parameter, which we interpret as the rapidity of the boundary.

arXiv:2012.08367Journal of High Energy PhysicsMar 1, 20210 citations

Exact physical quantities of the

{D}_2^{(2)}

spin chain model with generic open boundary conditions

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)}

D 2 2 model in different regimes of boundary parameters.

Spectrum of the quantum integrable

{D}_2^{(2)}

spin chain with generic boundary fields

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.

A bstract The Izergin-Korepin model is an integrable model with the simplest twisted quantum affine algebra U q (

{A}_2^{(2)}

A 2 2 ) symmetry. Applying the t - W method, we derive the homogeneous zeroes Bethe ansatz equations and the corresponding zeroes patterns of the Izergin-Korepin model with generic integrable boundaries. Based on these results, we analytically compute the surface energies and boundary excitations in different regimes of boundary parameters of the model. It is shown that in some regimes, correlation effect appears between two boundary fields.

Exact solution of the quantum integrable model associated with the twisted

{\mathrm{D}}_3^{(2)}

algebra

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.

Factorization identities and algebraic Bethe ansatz for

{D}_2^{(2)}

models

Abstract We express

{D}_2^{(2)}

D 2 2 transfer matrices as products of

{A}_1^{(1)}

A 1 1 transfer matrices, for both closed and open spin chains. We use these relations, which we call factorization identities, to solve the models by algebraic Bethe ansatz. We also formulate and solve a new integrable XXZ-like open spin chain with an even number of sites that depends on a continuous parameter, which we interpret as the rapidity of the boundary.