Operator spreading in quantum hardcore gases

In this article we study integrable quantum cellular automata (QHCG) with an arbitrary local Hilbert space dimension, and discuss the matrix product ansatz based approach for solving the dynamics of local operators analytically. Subsequently, we focus on the dynamics of operator spreading, in particular on the out-of-time ordered correlation functions (OTOCs) and on the operator weight spreading. Both of the quantities are believed to provide signifying features of integrable systems and quantum chaos. We show that in QHCG OTOCs spread diffusively and that in the limit of the large local Hilbert space dimension they increase linearly with time, despite their integrability. On the other hand, it was recently conjectured that operator weight front, which is associated with the extent of operators, spreads diffusively in both, integrable and generic systems, but its decay seems to differ in these two cases. We observe that the spreading of operator weight front in QHCG is markedly different from chaotic, generic integrable and free systems, as the front freezes in the long time limit.Comment: 19 pages, 5 figure