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.
 Adrien Signoles, Adrien Facon, Dorian Grosso, Igor Dotsenko, Serge Haroche, Jean-Michel Raimond, Michel Brune, and Sébastien Gleyzes, ``Confined quantum Zeno dynamics of a watched atomic arrow'' Nature Physics 10, 715–719 (2014).
 Kyrylo Snizhko, Parveen Kumar, and Alessandro Romito, ``Quantum Zeno effect appears in stages'' Phys. Rev. Research 2, 033512 (2020).
 L. M. Duan, M. D. Lukin, J. I. Cirac, and P. Zoller, ``Long-distance quantum communication with atomic ensembles and linear optics'' Nature 414, 413–418 (2001).
 Anders S. Sørensenand Klaus Mølmer ``Measurement Induced Entanglement and Quantum Computation with Atoms in Optical Cavities'' Phys. Rev. Lett. 91, 097905 (2003).
 C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, ``Measurement-induced entanglement for excitation stored in remote atomic ensembles'' Nature 438, 828–832 (2005).
 N. Roch, M. E. Schwartz, F. Motzoi, C. Macklin, R. Vijay, A. W. Eddins, A. N. Korotkov, K. B. Whaley, M. Sarovar, and I. Siddiqi, ``Observation of Measurement-Induced Entanglement and Quantum Trajectories of Remote Superconducting Qubits'' Phys. Rev. Lett. 112, 170501 (2014).
 Jia Kong, Ricardo Jiménez-Martínez, Charikleia Troullinou, Vito Giovanni Lucivero, Géza Tóth, and Morgan W. Mitchell, ``Measurement-induced, spatially-extended entanglement in a hot, strongly-interacting atomic system'' Nature Communications 11, 2415 (2020).
 N. Syassen, D. M. Bauer, M. Lettner, T. Volz, D. Dietze, J. J. García-Ripoll, J. I. Cirac, G. Rempe, and S. Dürr, ``Strong Dissipation Inhibits Losses and Induces Correlations in Cold Molecular Gases'' Science 320, 1329–1331 (2008).
 Y. S. Patil, S. Chakram, and M. Vengalattore, ``Measurement-Induced Localization of an Ultracold Lattice Gas'' Phys. Rev. Lett. 115, 140402 (2015).
 Heinrich Fröml, Alessio Chiocchetta, Corinna Kollath, and Sebastian Diehl, ``Fluctuation-Induced Quantum Zeno Effect'' Phys. Rev. Lett. 122, 040402 (2019).
 Heinrich Fröml, Christopher Muckel, Corinna Kollath, Alessio Chiocchetta, and Sebastian Diehl, ``Ultracold quantum wires with localized losses: Many-body quantum Zeno effect'' Phys. Rev. B 101, 144301 (2020).
 Brian Skinner, Jonathan Ruhman, and Adam Nahum, ``Measurement-Induced Phase Transitions in the Dynamics of Entanglement'' Phys. Rev. X 9, 031009 (2019).
 M. Szyniszewski, A. Romito, and H. Schomerus, ``Entanglement transition from variable-strength weak measurements'' Phys. Rev. B 100, 064204 (2019).
 Soonwon Choi, Yimu Bao, Xiao-Liang Qi, and Ehud Altman, ``Quantum Error Correction in Scrambling Dynamics and Measurement-Induced Phase Transition'' Phys. Rev. Lett. 125, 030505 (2020).
 Chao-Ming Jian, Yi-Zhuang You, Romain Vasseur, and Andreas W. W. Ludwig, ``Measurement-induced criticality in random quantum circuits'' Phys. Rev. B 101, 104302 (2020).
 Xhek Turkeshi, Rosario Fazio, and Marcello Dalmonte, ``Measurement-induced criticality in $(2+1)$-dimensional hybrid quantum circuits'' Phys. Rev. B 102, 014315 (2020).
 D. A. Ivanov, T. Yu. Ivanova, S. F. Caballero-Benitez, and I. B. Mekhov, ``Feedback-Induced Quantum Phase Transitions Using Weak Measurements'' Phys. Rev. Lett. 124, 010603 (2020).
 Dayou Yang, Andrey Grankin, Lukas M. Sieberer, Denis V. Vasilyev, and Peter Zoller, ``Quantum non-demolition measurement of a many-body Hamiltonian'' Nature Communications 11, 775 (2020).
 M. Grossand S. Haroche ``Superradiance: An essay on the theory of collective spontaneous emission'' Physics Reports 93, 301 –396 (1982).
 G. L. Celardoand L. Kaplan ``Superradiance transition in one-dimensional nanostructures: An effective non-Hermitian Hamiltonian formalism'' Phys. Rev. B 79, 155108 (2009).
 Naftali Auerbachand Vladimir Zelevinsky ``Super-radiant dynamics, doorways and resonances in nuclei and other open mesoscopic systems'' Reports on Progress in Physics 74, 106301 (2011).
 A. Biella, F. Borgonovi, R. Kaiser, and G. L. Celardo, ``Subradiant hybrid states in the open 3D Anderson-Dicke model'' EPL (Europhysics Letters) 103, 57009 (2013).
 William Guerin, Michelle O. Araújo, and Robin Kaiser, ``Subradiance in a Large Cloud of Cold Atoms'' Phys. Rev. Lett. 116, 083601 (2016).
 I Rotterand J P Bird ``A review of progress in the physics of open quantum systems: theory and experiment'' Reports on Progress in Physics 78, 114001 (2015).
 Adam Nahum, Sthitadhi Roy, Brian Skinner, and Jonathan Ruhman, ``Measurement and Entanglement Phase Transitions in All-To-All Quantum Circuits, on Quantum Trees, and in Landau-Ginsburg Theory'' PRX Quantum 2, 010352 (2021).
 Xhek Turkeshi, Alberto Biella, Rosario Fazio, Marcello Dalmonte, and Marco Schiró, ``Measurement-induced entanglement transitions in the quantum Ising chain: From infinite to zero clicks'' Phys. Rev. B 103, 224210 (2021).
 O. Alberton, M. Buchhold, and S. Diehl, ``Entanglement Transition in a Monitored Free-Fermion Chain: From Extended Criticality to Area Law'' Phys. Rev. Lett. 126, 170602 (2021).
 James M. Hickey, Sam Genway, Igor Lesanovsky, and Juan P. Garrahan, ``Time-integrated observables as order parameters for full counting statistics transitions in closed quantum systems'' Phys. Rev. B 87, 184303 (2013).
 Carl M Bender ``PT-symmetric quantum theory'' Journal of Physics: Conference Series 631, 012002 (2015).
 H. P. Breuerand F. Petruccione ``The theory of open quantum systems'' Oxford University Press (2002).
 A B Harris ``Upper bounds for the transition temperatures of generalized Ising models'' Journal of Physics C: Solid State Physics 7, 3082–3102 (1974).
 R B Stinchcombe ``Diluted quantum transverse Ising model'' Journal of Physics C: Solid State Physics 14, L263–L267 (1981).
 Foster Thompsonand Rajiv R. P. Singh ``Griffiths-McCoy singularities in the dilute transverse-field Ising model: A numerical linked cluster expansion study'' Phys. Rev. E 99, 032129 (2019).
 T. Senthiland Subir Sachdev ``Higher Dimensional Realizations of Activated Dynamic Scaling at Random Quantum Transitions'' Phys. Rev. Lett. 77, 5292–5295 (1996).
 Gregory S. Bentsen, Subhayan Sahu, and Brian Swingle, "Measurement-induced purification in large- N hybrid Brownian circuits", Physical Review B 104 9, 094304 (2021).
 Yuto Ashida, Zongping Gong, and Masahito Ueda, "Non-Hermitian physics", Advances in Physics 69 3, 249 (2020).
 M. Buchhold, Y. Minoguchi, A. Altland, and S. Diehl, "Effective Theory for the Measurement-Induced Phase Transition of Dirac Fermions", arXiv:2102.08381.
 Shao-Kai Jian, Zhi-Cheng Yang, Zhen Bi, and Xiao Chen, "Yang-Lee edge singularity triggered entanglement transition", arXiv:2101.04115.
 Sarang Gopalakrishnan and Michael J. Gullans, "Entanglement and Purification Transitions in Non-Hermitian Quantum Mechanics", Physical Review Letters 126 17, 170503 (2021).
 Xhek Turkeshi, Alberto Biella, Rosario Fazio, Marcello Dalmonte, and Marco Schiró, "Measurement-induced entanglement transitions in the quantum Ising chain: From infinite to zero clicks", Physical Review B 103 22, 224210 (2021).
 Elmer V. H. Doggen, Yuval Gefen, Igor V. Gornyi, Alexander D. Mirlin, and Dmitry G. Polyakov, "Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization", arXiv:2104.10451.
 Xhek Turkeshi, "Measurement-induced criticality as a data-structure transition", arXiv:2101.06245.
 Piotr Sierant, Giuliano Chiriacò, Federica M. Surace, Shraddha Sharma, Xhek Turkeshi, Marcello Dalmonte, Rosario Fazio, and Guido Pagano, "Dissipative Floquet Dynamics: from Steady State to Measurement Induced Criticality in Trapped-ion Chains", arXiv:2107.05669.
 Kevin T. Geier and Philipp Hauke, "From non-Hermitian linear response to dynamical correlations and fluctuation-dissipation relations in quantum many-body systems", arXiv:2104.03983.
 T. Boorman, M. Szyniszewski, H. Schomerus, and A. Romito, "Diagnosing entanglement dynamics in noisy and disordered spin chains via the measurement-induced steady-state entanglement transition", arXiv:2107.11354.
 Abhijit P. Chaudhari, Shane P. Kelly, Riccardo Javier Valencia Tortora, and Jamir Marino, "Zeno crossovers in the entanglement speed of spin chains with noisy impurities", arXiv:2103.16172.
 Piotr Sierant and Xhek Turkeshi, "Universal behavior beyond multifractality of wave-functions at measurement--induced phase transitions", arXiv:2109.06882.
 Sankhya Basu, Daniel P. Arovas, Sarang Gopalakrishnan, Chris A. Hooley, and Vadim Oganesyan, "Fisher zeros and persistent temporal oscillations in non-unitary quantum circuits", arXiv:2103.10628.
 Y. Minoguchi, P. Rabl, and M. Buchhold, "Continuous Gaussian Measurements of the Free Boson CFT: An Exactly Solvable Model", arXiv:2108.04256.
 Ji Zou, Shu Zhang, and Yaroslav Tserkovnyak, "Bell-state generation for spin qubits via dissipative coupling", arXiv:2108.07365.
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