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arXiv:2512.14830

Strong-to-weak symmetry breaking in monitored dipole conserving quantum circuits

Caterina Zerba, Sarang Gopalakrishnan, Michael Knap

quant-phcond-mat.stat-mechSubmitted Dec 16, 2025• Announced Dec 18, 2025• 0 citations
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Abstract

We explore the information-theoretic phases of monitored quantum circuits subject to dynamics that conserves both charge and dipole moment, as well as measurements of the local charge density. Explicitly, both charge and dipole-moment conservation are strong symmetries, but under the dynamics they can be spontaneously broken to weak symmetries: this spontaneous symmetry breaking has an information-theoretic interpretation in terms of whether one can learn global charges from local measurements. We find a rich phase diagram: in one spatial dimension, charge is always easy to learn, while dipole moment can be either easy or hard. In two dimensions, we find three phases: for frequent measurements, both charge and dipole moment are easy to learn; as the measurement rate is decreased, first dipole moment and then charge become hard. In two dimensions, the low-measurement phase is an exotic critical phase with anisotropic spacetime scaling, analogous to a smectic liquid crystal.

Comments
7+7 pages, 2 figures

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