Abstract

Co-authors: G. Niccoli (ENS Lyon), N. Kitanine (Univ. de Bourgogne), J.M. Maillet (ENS Lyon)

During the last decades, important progresses have been made concerning the computation of form factors and correlation functions of simple models solvable by algebraic Bethe Ansatz (ABA) such as the XXZ spin-1/2 chain or 1D Bose gas with periodic boundary conditions. However, the generalization of these results to more complicated models or different types of integrable boundary conditions is for the moment limited by the range of applicability of ABA or by some difficulties of the method.

In this talk, we discuss the solution of Heisenberg spin chains (XXX, XXZ or XYZ ) in the framework of a complementary approach, Sklyanin's quantum Separation of Variables approach. This enables us notably to consider for these models various types of boundary conditions (quasi-periodic, open…) not directly solvable by Bethe ansatz. More precisely, we discuss in this framework some new results and open problems concerning the description of the spectrum by means of solutions of a functional T-Q equation (or equivalently in terms of Bethe-type equations). We also discuss the problem of the computation of the eigenstates scalar products and of the form factors of local operators.