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Scalar products in models with GL(3) trigonometric R-matrix. General case

Pakuliak, S., E. Ragoucy, N. A. Slavnov

Published Jan 1, 2014• 10 citations
OpenAlex

Abstract

We study quantum integrable models with $GL(3)$ trigonometric $R$-matrixsolvable by the nested algebraic Bethe ansatz. We analyze scalar products ofgeneric Bethe vectors and obtain an explicit representation for them in termsof a sum with respect to partitions of Bethe parameters. This representationgeneralizes known formula for the scalar products in the models with$GL(3)$-invariant $R$-matrix.

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We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing gl(2∣1)\mathfrak{gl}(2|1)gl(2∣1) symmetry. Using explicit formulas of the monodromy matrix entries multiple actions onto Bethe vectors we obtain a representation for the scalar product in the most general case. This explicit representation appears to be a sum over partitions of the Bethe parameters. It can be used for the analysis of scalar products involving on-shell Bethe vectors. As a by-product, we obtain a determinant representation for the scalar products of generic Bethe vectors in integrable models with gl(1∣1)\mathfrak{gl}(1|1)gl(1∣1) symmetry.
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