Bistability and time crystals in long-ranged directed percolation.
Springer Science and Business Media LLC
MetadataShow full item record
Pizzi, A., Nunnenkamp, A., & Knolle, J. (2021). Bistability and time crystals in long-ranged directed percolation.. Nat Commun, 12 (1) https://doi.org/10.1038/s41467-021-21259-4
Funder: Royal Society; doi: https://doi.org/10.13039/501100000288
Stochastic processes govern the time evolution of a huge variety of realistic systems throughout the sciences. A minimal description of noisy many-particle systems within a Markovian picture and with a notion of spatial dimension is given by probabilistic cellular automata, which typically feature time-independent and short-ranged update rules. Here, we propose a simple cellular automaton with power-law interactions that gives rise to a bistable phase of long-ranged directed percolation whose long-time behaviour is not only dictated by the system dynamics, but also by the initial conditions. In the presence of a periodic modulation of the update rules, we find that the system responds with a period larger than that of the modulation for an exponentially (in system size) long time. This breaking of discrete time translation symmetry of the underlying dynamics is enabled by a self-correcting mechanism of the long-ranged interactions which compensates noise-induced imperfections. Our work thus provides a firm example of a classical discrete time crystal phase of matter and paves the way for the study of novel non-equilibrium phases in the unexplored field of driven probabilistic cellular automata.
Article, /639/766/119, /639/766/530, article
Royal Society (RGF/EA/180038)
Royal Society (URF\R\191001)
External DOI: https://doi.org/10.1038/s41467-021-21259-4
This record's URL: https://www.repository.cam.ac.uk/handle/1810/317729
Attribution 4.0 International (CC BY 4.0)
Licence URL: https://creativecommons.org/licenses/by/4.0/