TL;DR
This paper investigates the structure of Bethe vectors in generalized XXX and XXZ models, demonstrating their equivalence in coordinate and algebraic Bethe ansatzes for Heisenberg spin chains.
Contribution
It provides a detailed description of Bethe vectors in multi-component models and proves the equivalence of two main Bethe ansatz methods for these models.
Findings
Bethe vectors expressed in local variables and operators
Equivalence of coordinate and algebraic Bethe ansatzes established
Structural insights applicable to XXX and XXZ spin chains
Abstract
The structure of Bethe vectors for generalised models associated with the XXX- and XXZ-type R-matrix is investigated. The Bethe vectors in terms of two--component and multi--component models are described. Consequently, their structure in terms of local variables and operators is provided. This, as a consequence, proves the equivalence of coordinate and algebraic Bethe ansatzes for the Heisenberg XXX and XXZ spin chains.
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