Temporal entanglement, quasiparticles and the role of interactions

TL;DR

This paper investigates how interactions in quantum many-body systems influence temporal entanglement, revealing that interactions cause a logarithmic growth in entanglement over time, which challenges the efficiency of simulating such systems.

Contribution

It demonstrates that interactions in integrable quantum systems lead to a violation of the area law for temporal entanglement, showing a logarithmic growth instead of sublinear or constant behavior.

Findings

Temporal entanglement grows logarithmically with time in interacting systems.

Interactions cause violations of the area law for temporal entanglement.

Analytical and numerical evidence supports the growth behavior in the XXZ model.

Abstract

In quantum many-body dynamics admitting a description in terms of non-interacting quasiparticles, the Feynman-Vernon influence matrix (IM), encoding the effect of the system on the evolution of its local subsystems, can be analyzed exactly. For discrete dynamics, the temporal entanglement (TE) of the corresponding IM satisfies an area law, suggesting the possibility of an efficient representation of the IM in terms of matrix-product states. A natural question is whether and how integrable interactions, which preserve stable quasiparticles, affect the behavior of the TE. While a simple semiclassical picture suggests a sublinear growth in time, one can wonder whether interactions may lead to violations of the area law. We address this problem by analyzing quantum quenches in a family of discrete integrable dynamics corresponding to the real-time Trotterization of the interacting XXZ Heisenberg model. By means of an analytical solution at the dual-unitary point and numerical calculations for generic values of the system parameters, we provide evidence that, away from the non-interacting limit, the TE displays a logarithmic growth in time, thus violating the area law. Our findings highlight the non-trivial role of interactions, and raise interesting questions on the possibility to efficiently simulate the local dynamics of interacting integrable systems.