Disappearance of measurement-induced phase transition in a quantum spin system for large sizes

Abstract

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 $\tau$, 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 $\tau$ values, we compute the survival probability, entanglement in bipartition, and the generalized geometric measure, a genuine multiparty entanglement, for a chain of size $L\sim 26$, and identify a transition at ${\tau }_c\sim 0.2$ 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 ${\tau }_c\sim 1/\sqrt{L}$. The transition at finite \(τ_c\) for \(L \sim 28\) seems therefore to recede to \(τ_c = 0\) 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.

13 pages, 15 figures

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