Bistability and time crystals in long-ranged directed percolation

Andrea Pizzi, Andreas Nunnenkamp and Johannes Knolle ()
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Andrea Pizzi: University of Cambridge
Andreas Nunnenkamp: University of Nottingham
Johannes Knolle: Technische Universität München

Nature Communications, 2021, vol. 12, issue 1, 1-8

Abstract: 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 driven probabilistic cellular automata.

Date: 2021
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DOI: 10.1038/s41467-021-21259-4

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