Theoretical and Mathematical Physics

Action of the monodromy matrix elements in the generalized algebraic Bethe ansatz

G. Kulkarni, N. A. Slavnov

Published Dec 1, 2023• 2 citations

Abstract

We consider an $$XYZ$$ 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 $$8$$ -vertex model.

DOI: 10.1134/s0040577923120085

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Theoretical and Mathematical Physics

Action of the monodromy matrix elements in the generalized algebraic Bethe ansatz

G. Kulkarni, N. A. Slavnov

Published Dec 1, 2023• 2 citations

Publisher

Abstract

We consider an

XYZ

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

8

-vertex model.

DOI: 10.1134/s0040577923120085

Related papers

Action of the monodromy matrix entries in the generalized algebraic Bethe ansatz

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We consider an $XYZ$ 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 $XYZ$ 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.

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arXiv:2005.09249Journal of Statistical Mechanics Theory and ExperimentSep 1, 202012 citations

We consider an

XYZ

8

-vertex model.

We consider an

XYZ

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.

A note on

\mathfrak{g}{\mathfrak{l}}_2

-invariant Bethe vectors

Abstract We consider

\mathfrak{g}{\mathfrak{l}}_2

g l 2 -invariant quantum integrable models solvable by the algebraic Bethe ansatz. We show that the form of on-shell Bethe vectors is preserved under certain twist transformations of the monodromy matrix. We also derive the actions of the twisted monodromy matrix entries on the twisted off-shell Bethe vectors.