Complexity and quenches in models with three and four spin interactions

We study information theoretic quantities in models with three and four spin interactions. These models show distinctive characteristics compared to their nearest neighbour (NN) counterparts. Here, we quantify these in terms of the Nielsen complexity (NC) in static and quench scenarios, the Fubini-Study complexity (FSC), and the entanglement entropy (EE). The models that we study have a rich phase structure, and we show how the difference in the nature of phase transitions in these, compared to ones with NN interactions, result in different behaviour of information theoretic quantities, from ones known in the literature. For example, the derivative of the NC does not diverge but shows a discontinuity near continuous phase transitions, and the FSC may be regular and continuous across such transitions. We also study multiple quench scenarios in these models and contrast these with quenches in the transverse XY model. The EE shows a novel discontinuity both at first and second order quantum phase transitions.