On Form Factors in nested Bethe Ansatz systems

TL;DR

This paper analyzes the form factors of local operators in multi-component quantum integrable models solvable by nested Bethe Ansatz, providing analytic properties, recursion relations, and explicit solutions for specific cases.

Contribution

It introduces a detailed analysis of form factors in nested Bethe Ansatz systems, including recursion relations and explicit solutions for simple cases.

Findings

Derived analytic properties of form factors.

Established connection between infinite and finite volume form factors.

Obtained explicit solutions for one spin-impurity cases.

Abstract

We investigate form factors of local operators in the multi-component Quantum Non-linear Schr\"odinger 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.