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2023•Theoretical and Mathematical PhysicsOpen access

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

G. Kulkarni, N. A. Slavnov

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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.

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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 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.

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Available 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.

Key concepts: Bethe ansatz, Monodromy matrix, Monodromy, Mathematics, Thirring model, Mathematical physics, Algebraic number, Partition function (quantum field theory)

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