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Drinfeld twists and symmetric Bethe vectors of supersymmetric fermion models

Shao-you Zhao A, Wen‐Li Yang, Yao-Zhong Zhang

We construct the Drinfeld twists (factorizing F -matrices) of the gl ( m | n )-invariant fermion model. Completely symmetric representation of the pseudo-particle creation operators of the model are obtained in the basis provided by the F -matrix (the F -basis). We resolve the hierarchy of the nested Bethe vectors in the F -basis for the gl ( m | n ) supersymmetric model.

arXiv:nlin/0502050Journal of Statistical Mechanics Theory and ExperimentApr 13, 200514 citations

Polarization-free generators for the Belavin model

T.-D. Albert, K. Ruhlig

Employing a change of basis, the so-called factorizing Drinfel'd twist, we construct polarization-free and completely symmetric creation operators for a face type model equivalent to the Belavin model. A resolution of the nested structure of the Bethe vectors is achieved.

arXiv:nlin/0007020Journal of Physics A Mathematical and GeneralFeb 19, 200114 citations

Drinfeld twist and the domain wall partition function of the eight-vertex model

Kun Hao, Xi Chen, Kangjie Shi +1 more

With the help of the F -basis provided by the Drinfeld twist or factorising F -matrix for the spatial optical soliton model associated with the eight-vertex model, we calculate the partition function for the eight-vertex model on an N × N square lattice with domain wall boundary condition.

Chinese Physics BJan 1, 20111 citation

Bethe vectors and recurrence relations for twisted Yangian based models

Vidas Regelskis

We study Olshanski twisted Yangian based models, known as one-dimensional “soliton non-preserving” open spin chains, by means of algebraic Bethe Ansatz. The even case, when the bulk symmetry is \mathfrak{gl}_{2n} 𝔤 𝔩 2 n and the boundary symmetry is \mathfrak{sp}_{2n} 𝔰 𝔭 2 n or \mathfrak{so}_{2n} 𝔰 𝔬 2 n , was studied in [Ann. Henri Poincaré 20, 339 (2018)]. In the present work, we focus on the odd case, when the bulk symmetry is \mathfrak{gl}_{2n+1} 𝔤 𝔩 2 n + 1 and the boundary symmetry is \mathfrak{so}_{2n+1} 𝔰 𝔬 2 n + 1 . We explicitly construct Bethe vectors and present a more symmetric form of the trace formula. We use the composite model approach and Y(\mathfrak{gl}_n) Y ( 𝔤 𝔩 n ) -type recurrence relations to obtain recurrence relations for twisted Yangian based Bethe vectors, for both even and odd cases.We study Olshanski twisted Yangian based models, known as one-dimensional “soliton non-preserving” open spin chains, by means of algebraic Bethe Ansatz. The even case, when the bulk symmetry is \mathfrak{gl}_{2n} 𝔤 𝔩 2 n and the boundary symmetry is \mathfrak{sp}_{2n} 𝔰 𝔭 2 n or \mathfrak{so}_{2n} 𝔰 𝔬 2 n , was studied in [Ann. Henri Poincaré 20, 339 (2018)]. In the present work, we focus on the odd case, when the bulk symmetry is \mathfrak{gl}_{2n+1} 𝔤 𝔩 2 n + 1 and the boundary symmetry is \mathfrak{so}_{2n+1} 𝔰 𝔬 2 n + 1 . We explicitly construct Bethe vectors and present a more symmetric form of the trace formula. We use the composite model approach and Y(\mathfrak{gl}_n) Y ( 𝔤 𝔩 n ) -type recurrence relations to obtain recurrence relations for twisted Yangian based Bethe vectors, for both even and odd cases.

arXiv:2302.11842SciPost PhysicsNov 5, 20242 citations

Resolution of the nested hierarchy for rationalsl(n) models

T-D Albert, H Boos, R Flume +1 more

We construct Drinfel'd twists for the rational sl ( n ) XXX model giving rise to a completely symmetric representation of the monodromy matrix. We obtain a polarization-free representation of the pseudoparticle creation operators figuring in the construction of the Bethe vectors within the framework of the quantum inverse scattering method. This representation enables us to resolve the hierarchy of the nested Bethe ansatz for the sl ( n ) invariant rational Heisenberg model. Our results generalize the findings of Maillet and Sanchez de Santos for sl (2) models.We construct Drinfel'd twists for the rational sl ( n ) XXX model giving rise to a completely symmetric representation of the monodromy matrix. We obtain a polarization-free representation of the pseudoparticle creation operators figuring in the construction of the Bethe vectors within the framework of the quantum inverse scattering method. This representation enables us to resolve the hierarchy of the nested Bethe ansatz for the sl ( n ) invariant rational Heisenberg model. Our results generalize the findings of Maillet and Sanchez de Santos for sl (2) models.

arXiv:nlin/0002027Journal of Physics A Mathematical and GeneralJul 7, 200035 citations

The Drinfel'd twisted XYZ model

T.-D. Albert, Herman E. Boos, R. Flume +2 more

We construct a factorizing Drinfel'd twist for a face type model equivalent to the XYZ model. Completely symmetric expressions for the operators of the monodromy matrix are obtained.

arXiv:nlin/0005023May 11, 20002 citations

Drinfeld Twist and Symmetric Bethe Vectors of Open XYZ Chain with Non-Diagonal Boundary Terms

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Drinfeld Twist and Symmetric Bethe Vectors of Open XYZ Chain with Non-Diagonal Boundary Terms

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