2025/12/16 by Zerba, Caterina, Gopalakrishnan, Sarang, Knap, Michael
Computer Science · Physics and Astronomy · #FOS: Physical sciences #Quantum Computing Algorithms and Architecture #Quantum Physics (quant-ph) #Quantum many-body systems #Statistical Mechanics (cond-mat.stat-mech) #Topological Materials and Phenomena
paper · doi:10.48550/arxiv.2512.14830
openalex publication_date 2025/12/16 · openalex created_date 2025/12/19 · openalex updated_date 2026/07/28
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.