Complexity and quenches in models with three and four spin interactions

TL;DR

This paper investigates the behavior of information theoretic measures like Nielsen and Fubini-Study complexities and entanglement entropy in models with three and four spin interactions, revealing unique phase transition signatures and quench dynamics.

Contribution

It introduces the analysis of complexity and entanglement in multi-spin interaction models, highlighting differences from nearest neighbor models and their phase transition effects.

Findings

Discontinuity in Nielsen complexity derivative near continuous transitions

Fubini-Study complexity remains continuous across phase transitions

Entanglement entropy exhibits novel discontinuities at quantum phase transitions

Abstract

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