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Theoretical and Mathematical Physics

Form factors of local operators in the generalized algebraic Bethe ansatz

G. Kulkarni, N. A. Slavnov

Published Nov 1, 2024• 0 citations
Publisher

Abstract

We consider an $$XYZ$$ spin chain within the framework of the generalized algebraic Bethe ansatz. We study form factors of local operators corresponding to singlet states in the free-fermion limit. We obtain explicit representations for these form factors.

DOI
10.1134/s0040577924110102

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We consider an XYZXYZXYZ spin chain within the framework of the generalized algebraic Bethe ansatz. We study form factors of local operators corresponding to singlet states in the free-fermion limit. We obtain explicit representations for these form factors.
We consider an XYZXYZXYZ spin chain within the framework of the generalized algebraic Bethe ansatz. We study form factors of local operators corresponding to the singlet states in the limit of free fermions. We obtain explicit representations for these form factors.
We consider an XYZXYZXYZ spin chain within the framework of the generalized algebraic Bethe ansatz. We study scalar products of the transfer matrix eigenvectors and arbitrary Bethe vectors. In the particular case of free fermions, we obtain explicit expressions for the scalar products with different number of parameters in two Bethe vectors.
In this article we study the thermodynamic limit of the form factors of the XXX Heisenberg spin chain using the algebraic Bethe ansatz approach. Our main goal is to express the form factors for the low-lying excited states as determinants of matrices that remain finite dimensional in the thermodynamic limit. We show how to treat all types of the complex roots of the Bethe equations within this framework. In particular we demonstrate that the Gaudin determinant for the higher level Bethe equations arises naturally from the algebraic Bethe ansatz.
Abstract We apply the nested algebraic Bethe ansatz to the models with g l ( 2 | 1 ) and g l ( 1 | 2 ) supersymmetry. We show that form factors of local operators in these models can be expressed in terms of the universal form factors. Our derivation is based on the use of the RTT -algebra only. It does not refer to any specific representation of this algebra. We obtain thus determinant representations for form factors of local operators in the cases where an explicit solution of the quantum inverse scattering problem is not known.