Growth of entanglement of generic states under dual-unitary dynamics

TL;DR

This paper studies how entanglement grows in dual-unitary quantum circuits, showing that generic initial states lead to maximal entanglement growth in the long-time limit, extending known results from special solvable states.

Contribution

It demonstrates that even for generic initial states, dual-unitary circuits eventually achieve maximal entanglement growth, generalizing previous results limited to solvable states.

Findings

Entanglement growth approaches maximum in the infinite-time limit for generic states.

Sub-maximal entanglement growth occurs at finite times for generic states.

Rigorous proof provided for circuits with high entanglement generation.

Abstract

Dual-unitary circuits are a class of locally-interacting quantum many-body systems displaying unitary dynamics 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 non-equilibrium 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 sub-maximal 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.