Exact solutions of the C quantum spin chain

Li, Guangliang; Xue, Panpan; Sun, Pei; Yang, Haizhen; Xu, Xiaotian; Cao, Junpeng; Yang, Tao; Yang, Wen-Li

doi:10.1016/j.nuclphysb.2021.115333

Cited by 5 publications

(11 citation statements)

References 29 publications

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“…As a consequence of the commutativity property of the transfer matrices T (6) (λ), T (14) (λ) and T (14 ′ ) (λ), their common eigenvectors are independent of the spectral parameter λ. This implies that the relations (15)(16)(17)(18)(19) are also satisfied by the transfer matrix eigenvalues Λ (α) (λ), Λ (6) (λ)Λ (6)…”

Section: Fusion Relationsmentioning

confidence: 96%

“…where the projectors P (α) 12 are given in the Appendix B. This again shows explicitly the singular values that degenerate in projection operators, which can be exploited to derive the fusion hierarchy recursively (see [16] and the Appendix B for more details on the fusion hierarchy for Sp(2n) case). Nevertheless, it is not convenient for the general Sp(2n) case to label the spaces on which the R-matrices act in terms of the dimension of the representation.…”

Section: The General Sp(2n) Casementioning

confidence: 99%

“…This means that we can rewrite the fundamental R-matrix . By the rules of fusion [12,13,14], one can exploit the point λ = −1 to obtain a new R-matrix with a 14-dimensional auxiliary space (see [16,24] and the Appendix A for more details on the fusion rules for Sp(6)) given as, R (14,6) 12 (λ) = (λ − 3) P ′ (14) 12 + (λ + 3) P (70) 12 .…”

Section: Fusion Relationsmentioning

confidence: 99%

“…where ( 15) is the transfer matrix inversion identity [10] and O(e −L ) are corrections vanishing exponentially in the thermodynamic limit. The additional relations (16)(17)(18)(19) are derived along the same lines as [11] by exploiting the singular values…”

Section: Fusion Relationsmentioning

confidence: 99%

“…In order to do that, we first derive the transfer matrix fusion relations for the integrable Sp(6) vertex model. These relations hold for arbitrary values of the spectral parameter, which is in contrast with the discrete set of relations used in [16]. These fusion relations are naturally extended to the arbitrary Sp(2n) vertex model.…”

Section: Introductionmentioning

confidence: 99%

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On the partition function of the Sp(4) integrable vertex model

Ribeiro¹,

Klümper²,

Pearce³

2022

J. Stat. Mech.

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In this paper we investigate certain fusion relations associated to an integrable vertex model on the square lattice which is invariant under Sp(4) symmetry. We establish a set of functional relations which include a transfer matrix inversion identity. The solution of these relations in the thermodynamic limit allows us to compute the partition function per site of the fundamental Sp(4) representation of the vertex model. As a byproduct we also obtain the partition function per site of a vertex model mixing the four and five dimensional representations of the Sp(4) symmetry.

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Section: Fusion Relationsmentioning

confidence: 96%

Section: The General Sp(2n) Casementioning

confidence: 99%

Section: Fusion Relationsmentioning

confidence: 99%

Section: Fusion Relationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On the partition function of the Sp(4) integrable vertex model

Ribeiro¹,

Klümper²,

Pearce³

2022

J. Stat. Mech.

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Exact solution of the quantum integrable model associated with the twisted $$ {\mathrm{D}}_3^{(2)} $$ algebra

Hao

et al. 2022

J. High Energ. Phys.

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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.

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