Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits

Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of measurements, stemming from the competition between scrambling unitary dynamics and disentangling projective measurements. We study how entanglement dynamics in nonunitary quantum circuits can be enriched...

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Bibliographic Details
Published in:Physical review. X 2022-10, Vol.12 (4), p.041002, Article 041002
Main Authors: Agrawal, Utkarsh, Zabalo, Aidan, Chen, Kun, Wilson, Justin H., Potter, Andrew C., Pixley, J. H., Gopalakrishnan, Sarang, Vasseur, Romain
Format: Article
Language:English
Subjects:
Broken symmetry
Circuits
Coders
Conservation laws
Group theory
Interference
Legal issues
Mapping
Phase transitions
Quantum computing
Quantum entanglement
Quantum phenomena
Quantum theory
Robustness (mathematics)
Statistical analysis
Statistical mechanics
Symmetry
Thermalization (energy absorption)
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Summary:Monitored quantum circuits can exhibit an entanglement transition as a function of the rate of measurements, stemming from the competition between scrambling unitary dynamics and disentangling projective measurements. We study how entanglement dynamics in nonunitary quantum circuits can be enriched in the presence of charge conservation, using a combination of exact numerics and a mapping onto a statistical mechanics model of constrained hard-core random walkers. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement, distinguished by whether measurements can efficiently reveal the total charge of the system. We find that while Rényi entropies grow sub-ballistically astin the absence of measurement, for even an infinitesimal rate of measurements, all average Rényi entropies grow ballistically with time∼t. We study numerically the critical behavior of the charge-sharpening and entanglement transitions in U(1) circuits, and show that they exhibit emergent Lorentz invariance and can also be diagnosed using scalable local ancilla probes. Our statistical mechanical mapping technique readily generalizes to arbitrary Abelian groups, and offers a general framework for studying dissipatively stabilized symmetry-breaking and topological orders.
ISSN:2160-3308
2160-3308
DOI:10.1103/PhysRevX.12.041002