Non-equilibrium absorbing state phase transitions in discrete-time quantum cellular automaton dynamics on spin lattices

We introduce a discrete-time quantumdynamics on a two-dimensional lattice that describes the evolution of a 1+1-dimensional spin system. The underlying quantummap is constructed such that the reduced state at each time step is separable.We show that for long times this state becomes stationary and displays a continuous phase transition in the density of excited spins. This phenomenon can be understood through a connection to the so-calledDomany–Kinzel automaton, which implements a classical non-equilibriumprocess that features a transition to an absorbing state. Near the transition density–density correlations become long-ranged, and interestingly the same is the case for quantum correlations despite the separability of the stationary state.We quantify quantum correlations through the local quantumuncertainty and show that in some cases theymay be determined experimentally solely bymeasuring expectation values of classical observables. This work is inspired by recent experimental progress in the realization of Rydberg lattice quantum simulators, which—in a rather natural way—permit the realization of conditional quantum gates underlying the discrete-time dynamics discussed here.