Diffusion and operator entanglement spreading

Understand

Understanding the spreading of the operator space entanglement entropy ($OSEE$) is key in order to explore out-of-equilibrium quantum many-body systems.

• Here we argue that for integrable models the dynamics of the $OSEE$ is related to the diffusion of the underlying quasiparticles.
• We derive the logarithmic bound $1/2\ln(t)$ for the $OSEE$ of some simple, i.e., low-rank, diagonal local operators.
• We numerically check that the bound is saturated in the rule $54$ chain, which is representative of interacting integrable systems.