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We consider closed XXX spin chains with broken total spin $U(1)$ symmetry within the framework of the modified algebraic Bethe ansatz. We study multiple actions of the modified monodromy matrix entries on the modified Bethe vectors. The obtained formulas of the multiple actions allow us to calculate the scalar products of the modified Bethe vectors. We find an analog of Izergin-Korepin formula for the scalar products. This formula involves modified Izergin determinants and can be expressed as sums over partitions of the Bethe parameters.
We consider $mathfrak{gl}_2$-invariant quantum integrable models solvable by the algebraic Bethe ansatz. We show that the form of on-shell Bethe vectors is preserved under certain twist transformations of the monodromy matrix. We also derive the acti
We consider the overlap of Bethe vectors of the XXX spin chain with a diagonal twist and the modified Bethe vectors with a general twist. We find a determinant representation for this overlap under one additional condition on the twist parameters. Su
We explain how to compute correlation functions at zero temperature within the framework of the quantum version of the Separation of Variables (SoV) in the case of a simple model: the XXX Heisenberg chain of spin 1/2 with twisted (quasi-periodic) bou
The distribution of Bethe roots, solution of the inhomogeneous Bethe equations, which characterize the ground state of the periodic XXX Heisenberg spin-$frac{1}{2}$ chain is investigated. Numerical calculations shows that, for this state, the new inh
In this first paper, we start the analysis of correlation functions of quantum spin chains with general integrable boundary conditions. We initiate these computations for the open XXX spin 1/2 quantum chains with some unparallel magnetic fields allow