  Quantum systems evolving unitarily and subject to quantum measurements
exhibit various types of non-equilibrium phase transitions, arising from the
competition between unitary evolution and measurements. Dissipative phase
transitions in steady states of time-independent Liouvillians and measurement
induced phase transitions at the level of quantum trajectories are two primary
examples of such transitions. Investigating a many-body spin system subject to
periodic resetting measurements, we argue that many-body dissipative Floquet
dynamics provides a natural framework to analyze both types of transitions. We
show that a dissipative phase transition between a ferromagnetic ordered phase
and a paramagnetic disordered phase emerges for long-range systems as a
function of measurement probabilities. A measurement induced transition of the
entanglement entropy between volume law scaling and sub-volume law scaling is
also present, and is distinct from the ordering transition. The two phases
correspond to an error-correcting and a quantum-Zeno regimes, respectively. The
ferromagnetic phase is lost for short range interactions, while the volume law
phase of the entanglement is enhanced. An analysis of multifractal properties
of wave function in Hilbert space provides a common perspective on both types
of transitions in the system. Our findings are immediately relevant to trapped
ion experiments, for which we detail a blueprint proposal based on currently
available platforms.
