Growth of entanglement of generic states under dual-unitary dynamics

Dual-unitary circuits are a class of locally interacting quantum many-body systems displaying unitary dynamics also when the roles space and time exchanged. These have recently emerged as remarkable framework where certain features chaos can be studied exactly. In particular, they admit ``solvable'' initial states for which, in thermodynamic limit, one access full nonequilibrium dynamics. This reveals surprising property: dual-unitary circuit is prepared solvable state entanglement between two complementary spatial regions grows at maximal speed allowed by local structure evolution. Here we investigate fate this property system generic pair-product state. We show that case, increment during step submaximal finite times, however, it approaches value infinite-time limit. statement proven rigorously generating high enough entanglement, while argued to hold entire class.