Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 2. Determinant representation

Abstract

We study integrable models with $\mathfrak{gl}(2|1)$ symmetry and solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for scalar products of Bethe vectors, when the Bethe parameters obey some relations weaker than the Bethe equations. This representation allows us to find the norms of on-shell Bethe vectors and obtain determinant formulas for form factors of the diagonal entries of the monodromy matrix.

22 pages

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• Norm of Bethe vectors in models with $\mathfrak{gl}(m|n)$ symmetry
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Form factors of local operators in supersymmetric quantum integrable models
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Bethe Vectors for Composite Models with $\mathfrak{gl}(2|1)$ and $\mathfrak{gl}(1|2)$ Supersymmetry
• The LeClair-Mussardo series and nested Bethe Ansatz
• Scalar products and norm of Bethe vectors in ${\mathfrak{o}}_{2n+1}$ invariant integrable models
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• Quantum Integrability and Quantum Groups: a special issue in memory of Petr P. Kulish