Measurement-Induced Phase Transition for Large Systems

by Prof. Subinay Dasgupta (HRI Prayagraj)

Thursday 21 Aug 2025, 11:00 → 13:00 Asia/Kolkata

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We consider a quantum Ising chain going through a cycle of unitary time evolution followed by a measurement. The evolution is for a time τ under the transverse Ising Hamiltonian, and  the measurement (instantaneous) tests if all spins are up. It is found that for system size ≤ 28, there is a transition in entanglement at some critical value τ = τc. For extending our study to a larger size, we compute the survival probability of the initial state and find that coincident with the transition in entanglement, there appears a transition also in the derivative of the survival probability. We then prove analytically that the transition point τc for survival probability vanishes
for large system size as τc ∝ 1/√N and verify this numerically for size ≤ 1000. Hence, the transition in survival probability occurs only for a finite size for our protocol. It will be interesting to investigate the size-dependence of the critical point in the transition of entanglement in different systems.