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

Automated summary

Dual-unitary circuits are locally interacting quantum many-body systems that exhibit unitary dynamics even under the exchange of space and time. These systems have recently become a crucial framework for studying features of many-body quantum chaos exactly. In particular, they allow for a class of solvable initial states that provide access to the full nonequilibrium dynamics in the thermodynamic limit. It has been discovered that when a dual-unitary circuit is prepared in a solvable state, the quantum entanglement between two complementary spatial regions grows at the fastest possible rate determined by local evolution. In this study, we explore the behavior of this property when the system is in a generic pair-product state. We demonstrate that while the entanglement increment during a time step is submaximal for finite times in this case, it approaches the maximal value in the infinite-time limit. This result is rigorously proven for dual-unitary circuits that generate sufficiently high entanglement and is argued to hold for the entire class.