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We introduce a discrete-time quantum dynamics on a two-dimensional lattice that describes the evolution of a $1+1$-dimensional spin system. The underlying quantum map 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-called Domany-Kinzel automaton, which implements a classical non-equilibrium process that features a transition to an absorbing state. Near the transition density-density correlations become long-ranged, but interestingly the same is the case for quantum correlations despite the separability of the stationary state. We quantify quantum correlations through the local quantum uncertainty and show that in some cases they may be determined experimentally solely by measuring 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.
We present a formulation for investigating quench dynamics across quantum phase transitions in the presence of decoherence. We formulate decoherent dynamics induced by continuous quantum non-demolition measurements of the instantaneous Hamiltonian. W
Phase transitions to absorbing states are among the simplest examples of critical phenomena out of equilibrium. The characteristic feature of these models is the presence of a fluctuationless configuration which the dynamics cannot leave, which has p
Non-equilibrium aspects of the BCS model have fascinated physicists for decades, from the seminal works of Eliashberg to modern realizations in cold atom experiments. The latter scenarios have lead to a great deal of interest in the quench dynamics o
The effects of quenched disorder on nonequilibrium phase transitions in the directed percolation universality class are revisited. Using a strong-disorder energy-space renormalization group, it is shown that for any amount of disorder the critical be
Biological systems are typically highly open, non-equilibrium systems that are very challenging to understand from a statistical mechanics perspective. While statistical treatments of evolutionary biological systems have a long and rich history, exam