2025/01/29 by Chaki, Paranjoy, Nandi, Protyush, Sen, Ujjwal +1
#FOS: Physical sciences #Quantum Physics (quant-ph) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2501.17606
Measurement-induced phase transitions are often studied in random quantum circuits, with local measurements performed with a certain probability. We present here a model where a global measurement is performed with certainty at every time-step of the measurement protocol. Each time step, therefore, consists of evolution under the transverse Ising Hamiltonian for a time τ, followed by a measurement that provides a ``yes/no'' answer to the question, ``Are all spins up?''. The survival probability after n time-steps is defined as the probability that the answer is ``no'' in all the n time-steps. For various τ values, we compute the survival probability, entanglement in bipartition, and the generalized geometric measure, a genuine multiparty entanglement, for a chain of size L ∼ 26, and identify a transition at τc ∼ 0.2 for field strength h=1/2. We then analytically derive a recursion relation that enables us to calculate the survival probability for system sizes up to 1000, which provides evidence of a scaling τc ∼ 1/√(L). The transition at finite \(τc\) for \(L ∼ 28\) seems therefore to recede to \(τc = 0\) in the thermodynamic limit. Additionally, at large time-steps, survival probability decays logarithmically only when the ground state of the Hamiltonian is paramagnetic. Such decay is not present when the ground state is ferromagnetic.