Genuine Multipartite Correlations in a Boundary Time Crystal

TL;DR

This paper investigates the structure, dynamics, and scaling of genuine multipartite correlations in boundary time crystals, revealing persistent, oscillatory, and extensive correlations in the thermodynamic limit that distinguish them from non-time-crystal phases.

Contribution

It provides a detailed analysis of multipartite correlations in boundary time crystals, demonstrating their indefinite growth, oscillatory behavior, and extensive scaling, which are novel features of this non-equilibrium phase.

Findings

Multipartite correlations grow indefinitely in the thermodynamic limit.

Correlations display persistent oscillations around their mean.

GMCs scale extensively with system size in the time crystal phase.

Abstract

In this work we study genuine multipartite correlations (GMC's) in a boundary time crystal (BTC). Boundary time crystals are nonequilibrium quantum phases of matter in contact to an environment, for which a macroscopic fraction of the many-body system breaks the time-translation symmetry. We analyze both (i) the structure (orders) of GMC's among the subsystems, as well as (ii) their build-up dynamics for an initially uncorrelated state. We find that, in the thermodynamic limit (and only in such a limit), multipartite correlations of all orders grow indefinitely in time in the BTC phase, further displaying a persistent oscillatory behavior around their mean growth. The orders of the correlations show a power-law decaying hierarchy among its $k$-partitions. Moreover, in the long-time limit the GMC's are shown extensive with the system size, contrasting to the subextensive scaling in the non time-crystal (ferromagnetic) phase of the model. We also discuss the classical and quantum nature of these correlations with basis on multipartite entanglement witnesses, specifically, the analysis of the Quantum Fisher Information (QFI). Both GMC and QFI are able to capture and distinguish the different phases of the model. Our work highlights the genuine many-body properties of these peculiar non-equilibrium phases of matter.