Directed percolation in nonunitary quantum cellular automata

Directed percolation in nonunitary quantum cellular automata

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Probabilistic cellular automata (CA) provide a classic framework for studying nonequilibrium statistical physics on lattices.A notable example is the Domany-Kinzel CA, which has Ball - Miscellaneous been used to investigate the process of directed percolation and the critical dynamics of the nonequilibrium phase transition between absorbing and percolating phases.In this work, we construct a nonunitary quantum CA that generalizes the Domany-Kinzel CA and study the resulting dynamical evolution using numerical simulations using the tensor network infinite time-evolving block decimation (iTEBD) algorithm.

We demonstrate that the system undergoes the absorbing/percolating phase transition and that the addition of the Hamiltonian generates coherences, which are a distinct feature of quantum dynamics.A proposal for the implementation of the model with Rydberg array is put forward, which does not require local addressing COMPASS of individual sites.