Bistability and time crystals in long-ranged directed percolation

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. A model of a classical discrete time crystal satisfying the criteria of persistent subharmonic response robust against thermal noise and defects has been lacking. Here, the authors show that these criteria are satisfied in one-dimensional probabilistic cellular automata with long-range interactions and bistability.

Automated summary

The researchers introduced a simple cellular automaton model with power-law interactions, leading to a bistable phase of long-ranged directed percolation. They found that the system's response period is affected by periodic modulation. The self-correcting mechanism of long-ranged interactions can compensate for noise-induced imperfections.