Temporal Entanglement, Quasiparticles, and the Role of Interactions

Giacomo Giudice, Giuliano Giudici, Michael Sonner, Julian Thoenniss, Alessio Lerose, Dmitry A. Abanin, Lorenzo Piroli

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20 Scopus citations

Abstract

In quantum many-body dynamics admitting a description in terms of noninteracting 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 integrable interactions, preserving 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 noninteracting limit, the TE displays a logarithmic growth in time, thus violating the area law. Our findings highlight the nontrivial role of interactions, and raise interesting questions on the possibility to efficiently simulate the local dynamics of interacting integrable systems.

Original languageEnglish (US)
Article number220401
JournalPhysical review letters
Volume128
Issue number22
DOIs
StatePublished - Jun 3 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy

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