On form factors in nested Bethe Ansatz systems

Abstract

We investigate form factors of local operators in the multi-component Quantum Nonlinear Schrödinger model, a prototype theory solvable by the so-called nested Bethe Ansatz. We determine the analytic properties of the infinite volume form factors using the coordinate Bethe Ansatz solution and we establish a connection with the finite volume matrix elements. In the two-component models we derive a set of recursion relations for the "magnonic form factors", which are the matrix elements on the nested Bethe Ansatz states. In certain simple cases (involving states with only one spin-impurity) we obtain explicit solutions for the recursion relations.

Exact formulas for the form factors of local operators in the Lieb–Liniger model

“…. M ; (iv) the residues of the form factors are given by the following recursive relations Note that the recursive relation (42), first derived in [55], was also discussed in the recent papers [48,49,52]. In particular, in [48,49] its connection with recursive relations appearing in integrable quantum field theory were investigated.…”

“…In Ref. [52] techniques similar to those exploited in the present work were used to study form factors of local operators in systems solvable by Nested Bethe Ansatz.…”

“…It is given by the following proposition regarding some fundamental properties of the form factors of local operators [5,25,48,49,55,52].…”

“…Note that a similar approach was used in Ref. [52] for the study of local operators in nested Bethe Ansatz systems.…”

The algebraic Bethe ansatz for scalar products inSU(3)-invariant integrable models

“…There, an analog of IzerginKorepin formula for the scalar product of generic off-shell Bethe vectors and a determinant representation for the norm of the on-shell vectors were found. Recently various particular cases of scalar products were studied in [28][29][30][31].…”