Zamolodchikov–Faddeev algebra and quantum quenches in integrable field theories

We analyze quantum quenches in integrable models and in particular we determine the initial state in the basis of eigenstates of the post-quench Hamiltonian. This leads us to consider the set of transformations of creation and annihilation operators that respect the Zamolodchikov–Faddeev algebra satisfied by integrable models. We establish that the Bogoliubov transformations hold only in the case of quantum quenches in free theories. For the most general case of interacting theories, we identify two classes of transformations. The first class induces a change in the S -matrix of the theory but not in its ground state, whereas the second class results in a 'dressing' of the operators. We consider as examples of our approach the transformations associated with a change of the interaction in the sinh–Gordon model and the Lieb–Liniger model.