Replica Transition at Measurement-Altered Ising Criticality

Abstract:Performing measurements on gapless quantum ground states can give rise to new universal phenomena, whose origins remain poorly understood even for the paradigmatic Ising critical point. Replica methods offer a natural framework to study such post-measurement ensembles, with the replica limit $Q\to 1$ describing physical Born-averaged observables. Here we show that, for the monitored critical Ising chain, the replicated post-measurement ensemble of states itself undergoes a phase transition precisely at the physically relevant replica limit $Q \to 1$, preventing standard replica treatments. We use boundary conformal field theory (BCFT) methods to explain the underlying mechanism of this transition. Our methods yield a perturbative analytic calculation of the universal $O(1)$ constant in the Shannon entropy of the measurement record, previously known only numerically. We also apply our tools to study measurement-averaged spin correlators, providing a unified description of the universal properties of measurement outcomes and post-measurement states in the critical Ising chain.

Statistical Mechanics (cond-mat.stat-mech); Quantum Physics (quant-ph)

arXiv:2610.13802 [cond-mat.stat-mech]

(or arXiv:2610.13802v1 [cond-mat.stat-mech] for this version)

https://doi.org/10.48550/arXiv.2610.13802 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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