Operator spreading in quantum hardcore gases

In this article we study a set of integrable quantum cellular automata, the quantum hardcore gases (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), operator weight spreading and operators space entanglement entropy (OSEE). All of the quantities were conjectured 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 (Lopez-Piqueres et al 2021 Phys. Rev. B 104 104307). We observe that the spreading of the operator weight front in QHCG is markedly different from chaotic, generic integrable and free systems, as the front freezes in the long time limit. Finally, we discuss the OSEE in QHCG and show that it grows at most logarithmically with time in accordance with the conjectured behaviour for interacting integrable systems.