Zamolodchikov-Faddeev Algebra and Quantum Quenches in Integrable Field Theories

TL;DR

This paper investigates the structure of initial states after quantum quenches in integrable field theories, revealing that only free theories admit Bogoliubov transformations, while interacting theories involve more complex operator transformations.

Contribution

It characterizes the transformations of creation and annihilation operators compatible with the Zamolodchikov-Faddeev algebra in integrable models, distinguishing free and interacting cases.

Findings

Bogoliubov transformations only in free theories

Two classes of transformations in interacting theories

Application to Sinh-Gordon and Lieb-Liniger models

Abstract

We analyze quantum quenches in integrable models and in particular the determination of 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. In 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 of its ground state, whereas the second class results in a "dressing" of the operators. As examples of our approach we consider the transformations associated with a change of the interaction in the Sinh-Gordon and the Lieb-Liniger model.