Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries

Gombor, Tamás; Palla, L.

doi:10.1007/jhep02(2016)158

Cited by 4 publications

(6 citation statements)

References 31 publications

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“…From earlier results we know the Bethe Ansatz equations of the O(2N ) model with regular boundary conditions [10]. The result can be easily illustrated.…”

Section: Conventionsmentioning

confidence: 74%

“…Because of the complexity of the commutation relations of the elements of the transfer matrix we do not derive precisely the cancellation of unwanted terms. To check the correctness of the results we can compare the results of the subsections 3.2.5, 3.2.6, 3.2.7 with the previous results [10,2]. We then can assume that this method gives the correct result for the 4d case as well.…”

Section: Algebraic Bethe-ansatz For the O(2n ) Modelmentioning

confidence: 92%

“…It is possible because the R-matrix of the O(2N ) model has a six-vertex block-form. This method was generalized for open spin chains in [10]. Unfortunately, that procedure cannot be used for the model with O(2M +1)×O(2N −2M −1) symmetric boundary because its K-matrix is not block diagonal.…”

Section: Introductionmentioning

confidence: 99%

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Nonstandard Bethe Ansatz equations for open O(N) spin chains

Gombor

2018

Nuclear Physics B

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The double row transfer matrix of the open O(N ) spin chain is diagonalized and the Bethe Ansatz equations are also derived by the algebraic Bethe Ansatz method including the so far missing case when the residual symmetry is O(2M + 1) × O(2N − 2M − 1). In this case the boundary breaks the "rank" of the O(2N ) symmetry leading to nonstandard Bethe Ansatz equations in which the number of Bethe roots is less than as it was in the periodic case. Therefore these cases are similar to soliton-nonpreserving reflections.

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“…From earlier results we know the Bethe Ansatz equations of the O(2N ) model with regular boundary conditions [10]. The result can be easily illustrated.…”

Section: Conventionsmentioning

confidence: 74%

Section: Algebraic Bethe-ansatz For the O(2n ) Modelmentioning

confidence: 92%

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Nonstandard Bethe Ansatz equations for open O(N) spin chains

Gombor

2018

Nuclear Physics B

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“…where the charge conjugation of the reflection factor ensures the equivalence to equation (52) (see [24] for details). The diagonalization can be done either via the analytic [11] or the algebraic [25] Bethe Ansatz (BA). Results are available only for even N so we restrict ourselves to those cases.…”

Section: Bethe-yang Equationsmentioning

confidence: 99%

On integrable boundaries in the 2 dimensional O(N) σ-models

Aniceto¹,

Bajnok²,

Gombor³

et al. 2017

J. Phys. A: Math. Theor.

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We make an attempt to map the integrable boundary conditions for 2 dimensional nonlinear O(N) σ-models. We do it at various levels: classically, by demanding the existence of infinitely many conserved local charges and also by constructing the double row transfer matrix from the Lax connection, which leads to the spectral curve formulation of the problem; at the quantum level, we describe the solutions of the boundary Yang-Baxter equation and derive the Bethe-Yang equations. We then show how to connect the thermodynamic limit of the boundary Bethe-Yang equations to the spectral curve. arXiv:1706.05221v2 [hep-th]

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“…The exchange relations between these matrix operators turn out to be reminiscent of those of the six-vertex model. Such techniques have been used to study one-dimensional so 2n -and sp 2n -symmetric spin chains in [Rsh91,GP16,GR20,Rg22].…”

Section: Introductionmentioning

confidence: 99%

Bethe vectors and recurrence relations for twisted Yangian based models

Regelskis¹

2023

Preprint

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We study Olshanski twisted Yangian based models, known as one-dimensional "soliton nonpreserving" open spin chains, by means of the algebraic Bethe ansatz. The even case, when the underlying bulk Lie algebra is gl 2n , was studied in [GMR19]. In the present work, we focus on the odd case, when the underlying bulk Lie algebra is gl 2n+1 . We present a more symmetric form of the trace formula for Bethe vectors. We use the composite model approach and Y (gl n )-type recurrence relations to obtain recurrence relations for twisted Yangian based Bethe vectors, for both even and odd cases.

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Algebraic Bethe Ansatz for O(2N) sigma models with integrable diagonal boundaries

Cited by 4 publications

References 31 publications

Nonstandard Bethe Ansatz equations for open O(N) spin chains

Nonstandard Bethe Ansatz equations for open O(N) spin chains

On integrable boundaries in the 2 dimensional O(N) σ-models

Bethe vectors and recurrence relations for twisted Yangian based models

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