Genuine Multipartite Correlations in a Boundary Time Crystal

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.

Exact bistability and time pseudo-crystallization of driven-dissipative fermionic lattices

“…There are two recently introduced concepts, dissipative time crystals [27,[45][46][47][48][49][50][51][52][53][54][55][56][57][58], which are systems that have persistent oscillations induced by the dissipation, and boundary time crystals [59][60][61][62][63], which have persistent oscillations in the thermodynamic limit only (cf. discrete, driven versions of time crystals under dissipation [64][65][66][67][68][69][70] and other non-stationary phenomena beyond ob-servables e.g.…”

Dissipative time crystals originating from parity-time symmetry

“…On the other hand, in non-equilibrium systems such as Floquet systems [4][5][6][7][8] and dissipative systems [9][10][11][12][13][14][15][16][17][18][19][20][21][22], (discrete or dissipative) time crystals have been observed theoretically and experimentally. In dissipative systems with Lindblad dynamics, (dissipative) time crystals are characterized by the two conditions satisfied by the eigenvalues of the Liouvillian: (i) there exist pure imaginary eigenvalues iλ j and (ii) the quotient of each pure imaginary eigenvalue is a rational number λ j /λ k ∈ Q for all j, k [18].…”

“…However, the existence of dynamical symmetry is not necessary, and there exist time crystals which would have no dynamical symmetry. Among them time crystals that appear on the surface of a substance, called boundary time crystals (BTCs), have been actively investigated recently [10][11][12][13][14][15][16].…”