Operator spreading in quantum hardcore gases

In this article we study a set of integrable quantum cellular automata,the hardcore gases (QHCG), with an arbitrary local Hilbert space dimension, and discuss the matrix product ansatz based approach for solving dynamics operators analytically. Subsequently, focus on operator spreading, in particular out-of-time ordered correlation functions (OTOCs), weight spreading entanglement entropy (OSEE). All quantities were conjectured to provide signifying features systems chaos. We show that QHCG OTOCs spread diffusively limit large dimension they increase linearly time, despite their integrability. On other hand, it was recently front, which is associated extent operators, spreads both, generic systems, but its decay seems differ these two cases. observe front markedly different from chaotic, free as freezes long time limit. Finally, OSEE grows at most logarithmically accordance behaviour interacting systems.