Norm of Bethe vectors in models with $\mathfrak{gl}(m|n)$ symmetry

Abstract

We study quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(m|n)$-invariant $R$-matrix. We compute the norm of the Hamiltonian eigenstates. Using the notion of a generalized model we show that the square of the norm obeys a number of properties that uniquely fix it. We also show that a Jacobian of the system of Bethe equations obeys the same properties. In this way we prove a generalized Gaudin hypothesis for the norm of the Hamiltonian eigenstates.

LATEX, 24 pages, no figures, Proofs of proposition 5.1 and lemma 7.1 are clarified

References in corpus (3)

• Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
• Scalar products in GL(3)-based models with trigonometric R-matrix. Determinant representation
• Discrete CMC surfaces in R^3 and discrete minimal surfaces in S^3. A discrete Lawson correspondence

Cited by in corpus (11)

• Thermal form-factor approach to dynamical correlation functions of integrable lattice models
• On factorized overlaps: Algebraic Bethe Ansatz, twists, and Separation of Variables
• Inner products in integrable Richardson-Gaudin models
• On exact overlaps for $\mathfrak{gl}(N)$ symmetric spin chains
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• Solutions of ${\mathfrak{gl}}_{m|n}$ XXX Bethe ansatz equation and rational difference operators
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• Actions of the monodromy matrix elements onto $\mathfrak{gl}(m|n)$-invariant Bethe vectors
• On the supersymmetric XXX spin chains associated to ${\mathfrak{gl}}_{1|1}$
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Scalar products and norm of Bethe vectors in ${\mathfrak{o}}_{2n+1}$ invariant integrable models