Thermodynamic limit of the form factors of quantum spin chains

Exact computations of the correlation function is one of the most important subject of the theory of the quantum integrable models. An approach based on the calculation of form factors, i.e. matrix elements of the local spin operators, has been shown to be a more effective one. In this talk I will discuss a method based on algebraic Bethe ansatz for computing form factors of quantum spin chains in thermodynamic limit. We will consider the XXX model, which is one of the most simplest examples of quantum spin chain yet an interesting one as it belongs to the critical regime. For a particular case of form factors for excitations given by two spinons, we obtain an exact result in a closed-form using this method and find that it agrees with the previous result based on 𝑞-vertex operator algebra method. Generically however, excitations of the XXX ground state will also contain spinon bound states that are described by complex solutions of the Bethe equations. I will further elaborate on how this method can be generalized for such cases, leading to the determinant formulae for the thermodynamic form factors of any generic low-lying excitation, expressed in terms of the determinants of finite size.