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We introduce and investigate an open many-body quantum system in whichkinetically constrained coherent and dissipative processes compete. The form ofthe incoherent dissipative dynamics is inspired by that of epidemic spreadingor cellular-automaton-based computation related to the density-classificationproblem. It features two non-fluctuating absorbing states as well as a$\mathcal{Z}_2$-symmetric point in parameter space. The coherent evolution isgoverned by a kinetically constrained $\mathcal{Z}_2$-symmetric many-bodyHamiltonian which is related to the quantum XOR-Fredrickson-Andersen model. Weshow that the quantum coherent dynamics can stabilize a fluctuating state andwe characterize the transition between this active phase and the absorbingstates. We also identify a rather peculiar behavior at the$\mathcal{Z}_2$-symmetric point. Here the system approaches the absorbing-statemanifold with a dynamics that follows a power-law whose exponent continuouslyvaries with the relative strength of the coherent dynamics. Our work shows howthe interplay between coherent and dissipative processes as well as symmetryconstraints may lead to a highly intricate non-equilibrium evolution and maystabilize phases that are absent in related classical problems.

physical review. b./physical review. b

Signatures of a quantum stabilized fluctuating phase and critical  dynamics in a kinetically-constrained open many-body system with two  absorbing states