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

• URL: http://arxiv.org/abs/2110.00030v1
• Date: Thu, 30 Sep 2021 18:00:10 GMT
• Title: Exact solution of a boundary time-crystal phase transition: time-translation symmetry breaking and non-Markovian dynamics of correlations
• Authors: Federico Carollo and Igor Lesanovsky
• Abstract summary: Systems that display nonequilibrium transitions into these phases are referred to as time-crystals. We show that boundary time-crystals are intrinsically critical phases, where fluctuations exhibit a power-law divergence with time.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The breaking of the continuous time-translation symmetry manifests, in Markovian open quantum systems, through the emergence of non-stationary 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 non-linear and non-stationary (limit cycle) dynamics of a macroscopic order parameter. It is rather a genuine many-body phase where the properties of correlations distinctly differs from that of stationary ones.

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