Bistability and time crystals in long-ranged directed percolation

Pizzi, Andrea; Nunnenkamp, Andreas; Knolle, Johannes

Abstract

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 'Floquet probabilistic cellular automata'.

Citation

Pizzi, A., Nunnenkamp, A., & Knolle, J. (2021). Bistability and time crystals in long-ranged directed percolation. Nature Communications, 12, Article 1061. https://doi.org/10.1038/s41467-021-21259-4

• Journal Article Type: Article
• Acceptance Date: Jan 19, 2021
• Online Publication Date: Feb 16, 2021
• Publication Date: Feb 16, 2021
• Deposit Date: Jan 28, 2021
• Publicly Available Date: Feb 19, 2021
• Journal: Nature Communications
• Electronic ISSN: 2041-1723
• Publisher: Nature Publishing Group
• Peer Reviewed: Peer Reviewed
• Volume: 12
• Article Number: 1061
• DOI: https://doi.org/10.1038/s41467-021-21259-4
• Public URL: https://nottingham-repository.worktribe.com/output/5247197
• Publisher URL: https://www.nature.com/articles/s41467-021-21259-4