  It is well known that by repeatedly measuring a quantum system it is possible
to completely freeze its dynamics into a well defined state, a signature of the
quantum Zeno effect. Here we show that for a many-body system evolving under
competing unitary evolution and variable-strength measurements the onset of the
Zeno effect takes the form of a sharp phase transition. Using the Quantum Ising
chain with continuous monitoring of the transverse magnetization as
paradigmatic example we show that for weak measurements the entanglement
produced by the unitary dynamics remains protected, and actually enhanced by
the monitoring, while only above a certain threshold the system is sharply
brought into an uncorrelated Zeno state. We show that this transition is
invisible to the average dynamics, but encoded in the rare fluctuations of the
stochastic measurement process, which we show to be perfectly captured by a
non-Hermitian Hamiltonian which takes the form of a Quantum Ising model in an
imaginary valued transverse field. We provide analytical results based on the
fermionization of the non-Hermitian Hamiltonian in supports of our exact
numerical calculations.
