Zero modes method and form factors in quantum integrable models

Abstract

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing $GL(3)$-invariant $R$-matrix. Assuming that the monodromy matrix of the model can be expanded into series with respect to the inverse spectral parameter, we define zero modes of the monodromy matrix entries as the first nontrivial coefficients of this series. Using these zero modes we establish new relations between form factors of the elements of the monodromy matrix. We prove that all of them can be obtained from the form factor of a diagonal matrix element in special limits of Bethe parameters. As a result we obtain determinant representations for form factors of all the entries of the monodromy matrix.

24 pages; some misprints corrected

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• Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
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• GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors
• Form factors of local operators in a one-dimensional two-component Bose gas
• Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 2. Determinant representation
• Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models
• Form factors of the monodromy matrix entries in gl(2|1)-invariant integrable models
• Scalar products in GL(3)-based models with trigonometric R-matrix. Determinant representation
• Form factors of local operators in supersymmetric quantum integrable models
• Introduction to the nested algebraic Bethe ansatz
• Thermodynamics, density profiles and correlation functions of the inhomogeneous one-dimensional spinor Bose gas
• Algebraic Bethe ansatz
• Asymptotic behaviour of two-point functions in multi-species models
• 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
• Scalar products and norm of Bethe vectors in ${\mathfrak{o}}_{2n+1}$ invariant integrable models
• One-dimensional two-component Bose gas and the algebraic Bethe ansatz
• Bethe vectors and form factors for two-component Bose gas
• One-particle spectral function singularities in a one-dimensional gas of spin-1/2 fermions with repulsive delta-function interaction