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Scalar products in models with GL(3) trigonometric R-matrix. Determinant representation

N. A. Slavnov

Published Jan 26, 2015• 2 citations
OpenAlex

Abstract

We study quantum integrable models with the GL(3) trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. We derive a determinant representation for a special case of scalar products of Bethe vectors. This representation allows one to find a determinant formula for form factor of one of the monodromy matrix entries. We also point out essential difference between form factors in the models with the Gl(3) trigonometric R-matrix and their analogs in GL(3)-invariant models.

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We study quantum integrable models with the GL(3) trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. We derive a determinant representation for a special case of scalar products of Bethe vectors. This representation allows one to find a determinant formula for form factor of one of the monodromy matrix entries. We also point out essential difference between form factors in the models with the Gl(3) trigonometric R-matrix and their analogs in GL(3)-invariant models.
We study quantum integrable models with GL(3)GL(3)GL(3) trigonometric RRR-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 withGL(3)GL(3)GL(3)-invariant RRR-matrix.