Integrable open spin chains with nonsymmetric R-matrices

Mezincescu, Luca; Nepomechie, Rafael I.

doi:10.1088/0305-4470/24/1/005

Cited by 159 publications

(224 citation statements)

References 11 publications

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“…In this letter, we shall derive the reflection K-matrices, solutions of the boundary graded YB equation [66][67][68][69][70] (17) (also know as the graded reflection equation) for the YangZhang model [1]. In (17), R 12 denotes just the R-matrix defined on End (V ⊗ V ) and R 21 = P g R 12 P g ; besides, the reflection K-matrix is defined in End (V ), while…”

Section: (Although Its Hamiltonianmentioning

confidence: 99%

Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)
Vieira
¹
,
Santos
²

2017
Physics Letters A
2
0
3
0
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We derive the solutions of the boundary Yang-Baxter equation associated with a supersymmetric nineteen vertex model constructed from the three-dimensional representation of the twisted quantum affine Lie superalgebra U q [osp (2|2) (2) ]U q [C (2) (2) ]. We found three classes of solutions. The type I solution is characterized by three boundary free-parameters and all elements of the corresponding reflection K-matrix are different from zero. In the type II solution, the reflection K-matrix is even (every element of the K-matrix with an odd parity is null) and it has only one boundary free-parameter. Finally, the type III solution corresponds to a diagonal reflection K-matrix with two boundary free-parameters. The modelThis letter concerns with the reflection K-matrices of a supersymmetric nineteen vertex model introduced by Yang and Zhang in [1] (see also [2][3][4][5]). The Yang-Zhang R-matrix is constructed from a three-dimensional representation V of the twisted quantum affine Lie superalgebra(2) ], and the periodic algebraic Bethe Ansatz of this vertex model was performed in [6].Vertex models with underlying symmetries corresponding to Lie superalgebras are important in several fields of physics and mathematics. For instance, Z 2 -graded Lie superalgebras appear in the study of lattice models of strongly correlated electrons, such as the supersymmetric generalizations of the t-J model [7][8][9][10][11] and the Hubbard model [12,13], among others. The integrability of supersymmetric two-dimensional quantum chains had proved to be important as well in the AdS/CFT correspondence, either in the N = 4 super Yang-Mills side of the duality [14][15][16], or in the AdS 5 × S 5 string theory side [17]. Furthermore, these mathematical structures also are important in the construction of supersymmetric Hopf algebras and quantum groups [18][19][20][21] [30]. Considering now nonperiodic boundary conditions, the diagonal K-matrices for the ZFvm were first derived in [31] and the general Kmatrices were deduced in [32] and [33]; for the IKvm, the diagonal K-matrices were found in [34] and the general K-matrices were derived in [33] and [35]; besides, the coordinate Bethe Ansätze for both models were presented in [36], while their algebraic versions were performed in [37] (although the ZFvm had been considered before in [31] with the help of the fusion procedure [26]). Among the ZFvm and IKvm, other nineteen vertex models were discovered since then, for instance, the supersymmetric vertex models associated with the sl (2|1) and osp (2|1) Lie superalgebras, whose R-matrix was presented in [38] and the corresponding reflection K-matrices were obtained in [33]; for the Bethe Ansätze of these models, see [36,39]. Finally, other more complex nineteen vertex models were also discovered in the last decade − see, for instance, [40][41][42][43][44][45].The supersymmetric nineteen vertex model which we consider here is not included in the list above. The Rmatrix associated with this model was constructed in [1] and it can be wri...

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Section: (Although Its Hamiltonianmentioning

confidence: 99%

Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)
Vieira
¹
,
Santos
²

2017
Physics Letters A
2
0
3
0
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“…This boundary QISM uses a new algebraic structure, the reflection equation (RE) algebra. The solutions to the RE and its dual are called boundary K-matrices which in turn give rise to boundary conditions compatible with the integrability of the bulk model [6,7,8].…”

Section: Introductionmentioning

confidence: 99%

Multiple reference states and complete spectrum of the Belavin model with open boundaries

Yang

Zhang

2008

Nuclear Physics B

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The multiple reference state structure of the Z n Belavin model with non-diagonal boundary terms is discovered. It is found that there exist n reference states, each of them yields a set of eigenvalues and Bethe Ansatz equations of the transfer matrix. These n sets of eigenvalues together constitute the complete spectrum of the model. In the quasi-classic limit, they give the complete spectrum of the corresponding Gaudin model.

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“…For the graded case the YB equation R 12 (u)R 13 (u + v)R 23 (v) = R 23 (v)R 13 (u + v)R 12 (u) (1.4) and the reflection equation [8,9]…”

Section: Introductionmentioning

confidence: 99%

Algebraic Bethe ansatz solutions for thesl(2|1)⁽²⁾andosp(2|1) models with boundary terms

Kurak¹,

Lima-Santos²

2005

J. Phys. A: Math. Gen.

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This work is concerned with the formulation of the graded quantum inverse scattering method for a class of lattice models with reflecting boundary conditions. The sl(2|1) (2) and osp(2|1) models are considered with their diagonal reflections in BFB grading. This allowed us to derive the eigenvalues and eigenvectors for the corresponding transfer matrices as well as explicit expressions for the Bethe Ansatz equations.

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Integrable open spin chains with nonsymmetric R-matrices

Cited by 159 publications

References 11 publications

Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)
Vieira
¹
,
Santos
²

2017
Physics Letters A
2
0
3
0
View full text Add to dashboard Cite

Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)
Vieira
¹
,
Santos
²

2017
Physics Letters A
2
0
3
0
View full text Add to dashboard Cite

Multiple reference states and complete spectrum of the Belavin model with open boundaries

Algebraic Bethe ansatz solutions for thesl(2|1)⁽²⁾andosp(2|1) models with boundary terms

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Integrable open spin chains with nonsymmetric R-matrices

Cited by 159 publications

References 11 publications

Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)Vieira1, Santos2 2017Physics Letters A2030View full textAdd to dashboardCite

Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)Vieira1, Santos2 2017Physics Letters A2030View full textAdd to dashboardCite

Multiple reference states and complete spectrum of the Belavin model with open boundaries

Algebraic Bethe ansatz solutions for thesl(2|1)(2)andosp(2|1) models with boundary terms

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Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)
Vieira
¹
,
Santos
²

2017
Physics Letters A
2
0
3
0
View full text Add to dashboard Cite

Reflection K-matrices for a nineteen vertex model with Uq[osp(2|2)
Vieira
¹
,
Santos
²

2017
Physics Letters A
2
0
3
0
View full text Add to dashboard Cite

Algebraic Bethe ansatz solutions for thesl(2|1)⁽²⁾andosp(2|1) models with boundary terms