Exact solution of a boundary time-crystal phase transition: Time-translation symmetry breaking and non-Markovian dynamics of correlations

Carollo, Federico; Lesanovsky, Igor

Abstract

The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of nonstationary dynamical phases. Systems that display nonequilibrium transitions into these phases are referred to as time crystals, and they can be realized, for example, in many-body systems governed by collective dissipation and long-ranged interactions. Here, we provide a complete analytical characterization of a boundary time-crystal phase transition. This involves exact expressions for the order parameter and for the dynamics of quantum fluctuations, which, in the time-crystalline phase, remains asymptotically non-Markovian as a consequence of the time-translation symmetry breaking. We demonstrate that boundary time crystals are intrinsically critical phases, where fluctuations exhibit a power-law divergence with time. Our results show that a dissipative time-crystal phase is far more than merely a classical nonlinear and nonstationary (limit cycle) dynamics of a macroscopic order parameter. It is rather a genuine many-body phase where the properties of correlations distinctly differ from those of stationary ones.

• Journal Article Type: Article
• Acceptance Date: Apr 7, 2022
• Online Publication Date: Apr 22, 2022
• Publication Date: Apr 1, 2022
• Deposit Date: May 17, 2022
• Publicly Available Date: May 23, 2022
• Journal: Physical Review A
• Print ISSN: 2469-9926
• Electronic ISSN: 2469-9934
• Publisher: American Physical Society (APS)
• Peer Reviewed: Peer Reviewed
• Volume: 105
• Issue: 4
• Article Number: L040202
• DOI: https://doi.org/10.1103/PhysRevA.105.L040202
• Public URL: https://nottingham-repository.worktribe.com/output/7787405
• Publisher URL: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.105.L040202