arXiv:2202.06531 · Journal of High Energy Physics

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

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

Published Apr 19, 2022• 6 citations

Abstract

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.

DOI: 10.1007/jhep04(2022)101

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arXiv:2202.06531 · Journal of High Energy Physics

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

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

Published Apr 19, 2022• 6 citations

arXiv HTML PDF

Abstract

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.

DOI: 10.1007/jhep04(2022)101

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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.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.

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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)}

D 2 2 model are derived via off-diagonal Bethe ansatz.

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 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.

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.

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.