Quantum measurements cause an abrupt change, called measurement-induced phase transition, in the scaling behavior of entanglement entropy in a quantum many-body system. The phenomenon is often studied in random quantum circuits, with local measurements performed with a certain probability. We report here one such transition in an interacting spin-1/2 system where a global measurement is performed with certainty at every time step. We start with a pure state with all the spins up. Each time step consists of evolution under the transverse Ising Hamiltonian for a time $\tau$, followed by a measurement that provides a “yes or no” answer to the question “Are all spins up?”. For various $\tau$ values, we compute the survival probability of the inital state, entanglement in bipartition, and the generalized geometric measure (a genuine multiparty entanglement), for a chain of size $L\sim 28$, and identify the transition points ${\tau }_c$ for different field strengths. We then analytically derive a recursion relation that enables us to calculate the survival probability for system sizes up to 1000 and provides evidence of a scaling ${\tau }_c\sim 1/\sqrt{L}$. Therefore, the transition at finite ${\tau }_c$ for $L\sim 28$ seems to recede to ${\tau }_c=0$ in the thermodynamic limit. Our work prompts a widespread investigation on the existence of measurement-induced transitions at large system size.

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• Quantum measurements
• Quantum phase transitions
• Quantum many-body systems
• Quantum spin chains