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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