Quantum Fisher information in non-interacting systems after a sudden quench

In a recent study concerning the multipartite entanglement structure in states satisfying the eigenstate thermalization hypothesis (ETH), a measure known as the quantum Fisher information (QFI) was observed to detect differences in the entanglement content between thermal states of the same temperature; thus establishing a new, distinct way to distinguish between thermal states of different types (pure or mixed). In this work, we try to extend the previous analysis to the class of integrable models–i.e., systems which do not thermalize in the conventional way. We start this investigation with the simplest case, that of noninteracting systems. We derive exact analytic expressions of the QFI for a state described by the generalized Gibbs ensemble (GGE) and for a quenched pure state. We then show through various examples that this hierarchy of entanglement content persists