Measurement-induced criticality for non-Abelian anyons: The monitored golden chain
Abstract
Non-Abelian anyon chains whose interactions favor a single fusion channel host quantum critical ground states described by minimal-model conformal field theories (CFTs) protected by a topological symmetry. We show that their measurement-only counterpart, where non-commuting fusion charge measurements act locally on the anyons of a chain of L sites, provides a fundamental example of a non-unitary CFT controlling a non-Abelian learning problem. Mapping the monitored dynamics to a random tensor network, we numerically find 1/L scaling Lyapunov gaps, logarithmic entanglement scaling with the chord length, and an effective central charge in the Shannon entropy of the measurement record. The conserved topological charge sharpens with dynamical exponent z= 1 and is learnable by a decoder on an O(L) time scale. As the topological symmetry is a non-invertible symmetry of the SU(2)k anyon theories, we establish the monitored golden chain (k=3) as a non-Abelian generalization of the weakly (Kramers-Wannier) self-dual quantum critical point of the toric code (k=2), and the first of a family for k≥ 3.
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BibTeX
@misc{zhi2026measurementinduced,
title = {{Measurement-induced criticality for non-Abelian anyons: The monitored golden chain}},
author = {Zhaohui Zhi and Bo Han and Romain Vasseur and Andreas W. W. Ludwig and Simon Trebst and Guo-Yi Zhu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18965},
eprint = {2610.18965},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18965},
}
RIS
TY - UNPB
TI - Measurement-induced criticality for non-Abelian anyons: The monitored golden chain
AU - Zhaohui Zhi
AU - Bo Han
AU - Romain Vasseur
AU - Andreas W. W. Ludwig
AU - Simon Trebst
AU - Guo-Yi Zhu
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18965
UR - https://arxiv.org/abs/2610.18965
AB - Non-Abelian anyon chains whose interactions favor a single fusion channel host quantum critical ground states described by minimal-model conformal field theories (CFTs) protected by a topological symmetry. We show that their measurement-only counterpart, where non-commuting fusion charge measurements act locally on the anyons of a chain of L sites, provides a fundamental example of a non-unitary CFT controlling a non-Abelian learning problem. Mapping the monitored dynamics to a random tensor network, we numerically find 1/L scaling Lyapunov gaps, logarithmic entanglement scaling with the chord length, and an effective central charge in the Shannon entropy of the measurement record. The conserved topological charge sharpens with dynamical exponent z= 1 and is learnable by a decoder on an O(L) time scale. As the topological symmetry is a non-invertible symmetry of the SU(2)_k anyon theories, we establish the monitored golden chain (k=3) as a non-Abelian generalization of the weakly (Kramers-Wannier) self-dual quantum critical point of the toric code (k=2), and the first of a family for k≥ 3.
ER -