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arXiv:1911.08385 · Nuclear Physics B

Spinorial R operator and Algebraic Bethe Ansatz

David Roudolph Karakhanyan, R. Kirschner

Published Dec 19, 2019• 10 citations
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Abstract

We propose a new approach to the spinor-spinor R-matrix with orthogonal and symplectic symmetry. Based on this approach and the fusion method we relate the spinor-vector and vector-vector monodromy matrices for quantum spin chains. We consider the explicit spinor R matrices of low rank orthogonal algebras and the corresponding RTT algebras. Coincidences with fundamental R matrices allow to relate the Algebraic Bethe Ansatz for spinor and vector monodromy matrices.

DOI
10.1016/j.nuclphysb.2019.114905

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We propose a new approach to the spinor-spinor R-matrix with orthogonal and symplectic symmetry. Based on this approach and the fusion method we relate the spinor-vector and vector-vector monodromy matrices for quantum spin chains. We consider the explicit spinor R matrices of low rank orthogonal algebras and the corresponding RTT algebras. Coincidences with fundamental R matrices allow to relate the Algebraic Bethe Ansatz for spinor and vector monodromy matrices.
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Abstract We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing -invariant R -matrix. We study two types of Bethe vectors. The first type corresponds to the original monodromy matrix. The second type is associated to a monodromy matrix closely related to the inverse of the monodromy matrix. We show that these two types of Bethe vectors are identical up to normalization and reshuffling of the Bethe parameters. To prove this correspondence we use the current approach. This identity gives new combinatorial relations for the scalar products of the Bethe vectors. The q -deformed case, as well as the superalgebra case, are also evoked in the conclusion.
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We consider an XYZXYZXYZ spin chain within the framework of the generalized algebraic Bethe ansatz. We calculate the actions of monodromy matrix elements on Bethe vectors as a linear combination of new Bethe vectors. We also compute the multiple action of the gauge transformed monodromy matrix elements on the pre-Bethe vector and conceive the result in terms of a partition function of the 8-vertex model.
We consider an XYZXYZXYZ spin chain within the framework of the generalized algebraic Bethe ansatz. We calculate the actions of monodromy matrix elements on Bethe vectors as linear combinations of new Bethe vectors. We also compute the multiple action of the gauge-transformed monodromy matrix elements on the pre-Bethe vector and express the results in terms of the partition function of the 888 -vertex model.