Zamolodchikov–Faddeev algebra and quantum quenches in integrable field theories

Abstract

We analyze quantum quenches in integrable models and in particular we determine theinitial state in the basis of eigenstates of the post-quench Hamiltonian. This leads us toconsider the set of transformations of creation and annihilation operators thatrespect the Zamolodchikov–Faddeev algebra satisfied by integrable models. Weestablish that the Bogoliubov transformations hold only in the case of quantumquenches in free theories. For the most general case of interacting theories, weidentify two classes of transformations. The first class induces a change in theS-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 transformationsassociated with a change of the interaction in the sinh–Gordon model and the Lieb–Linigermodel.