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→ 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 → 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.
Related
- Practical roadmap to measurement-altered criticality in Rydberg arrays
- Quantum Ising transition on the Cayley tree: boundary criticality, universality, and an effective Bethe line
- Meson spectroscopy of exotic symmetries of Ising criticality in Rydberg atom arrays
- Meson Spectroscopy of Exotic Symmetries of Ising Criticality in Rydberg Atom Arrays
- Criticality without Temperature in an Ising Spin System
BibTeX
@misc{khanna2026replica,
title = {{Replica Transition at Measurement-Altered Ising Criticality}},
author = {Kabir Khanna and Sara Murciano and Romain Vasseur},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.13802},
eprint = {2610.13802},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.13802},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Replica Transition at Measurement-Altered Ising Criticality
AU - Kabir Khanna
AU - Sara Murciano
AU - Romain Vasseur
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2610.13802
UR - https://arxiv.org/abs/2610.13802
AB - 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→ 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 → 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.
ER -