Entanglement structure for finite system under dual-unitary dynamics

TL;DR

This paper explores how dual-unitary circuits influence entanglement growth in quantum many-body systems, revealing the impact of local unitaries and initial states on entanglement dynamics and bounds.

Contribution

It provides a detailed analysis of entanglement generation in dual-unitary circuits, including bounds and the role of local unitaries, advancing understanding of chaotic quantum dynamics.

Findings

Local unitaries significantly affect entanglement growth rates.

Time-step-dependent lower bounds on entanglement depend on initial states.

States evolved from pair products approach maximal multipartite entanglement.

Abstract

The dynamics of quantum many-body systems in the chaotic regime are of particular interest due to the associated phenomena of information scrambling and entanglement generation within the system. While these systems are typically intractable using traditional numerical methods, an effective framework can be implemented based on dual-unitary circuits which have emerged as a minimal model for maximally chaotic dynamics. In this work, we investigate how individual two-body operators influence the global dynamics of circuits composed of dual-unitaries. We study their effect on entanglement generation while examining it from both bipartite and multipartite perspectives. Here we also highlight the significant role of local unitaries in the dynamics when paired with operators from the dual-unitary class, showing that systems with identical entangling power can exhibit a range of differing entanglement growth rates. Furthermore, we present calculations establishing time-step-dependent lower bounds, which depend on both the initial state and the entangling power of the constituent operators. Finally, we find that time-evolving an initial state composed of pair products generates a state with nearly maximal multipartite entanglement content, approaching the bounds established by Absolutely Maximally Entangled (AME) states.