@article{8fe6c86106cf4568b9528f7b46347fe2,
title = "Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits",
abstract = "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 R{\'e}nyi entropies grow sub-ballistically as t in the absence of measurement, for even an infinitesimal rate of measurements, all average R{\'e}nyi 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.",
author = "Utkarsh Agrawal and Aidan Zabalo and Kun Chen and Wilson, {Justin H.} and Potter, {Andrew C.} and Pixley, {J. H.} and Sarang Gopalakrishnan and Romain Vasseur",
note = "Funding Information: We thank Michael Gullans, David Huse, Chaoming Jian, Vedika Khemani, and Andreas Ludwig for useful discussions and collaborations on related projects. We acknowledge support from NSF DMR-1653271 (S. G.), NSF DMR-1653007 (A. C. P.), the U.S. Air Force Office of Scientific Research under Grant No. FA9550-21-1-0123 (R. V.), and the Alfred P. Sloan Foundation through Sloan Research Fellowships (A. C. P., J. H. P., and R. V.). A. Z. and J. H. P. are partially supported by Grant No. 2018058 from the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel. A. Z. is partially supported through a Fellowship from the Research Discovery Informatics Institute. The Flatiron Institute is a division of the Simons Foundation. Funding Information: We thank Michael Gullans, David Huse, Chaoming Jian, Vedika Khemani, and Andreas Ludwig for useful discussions and collaborations on related projects. We acknowledge support from NSF DMR-1653271 (S. G.), NSF DMR-1653007 (A. C. P.), the U.S. Air Force Office of Scientific Research under Grant No. FA9550-21-1-0123 (R. V.), and the Alfred P. Sloan Foundation through Sloan Research Fellowships (A. C. P., J. H. P., and R. V.). A. Z. and J. H. P. are partially supported by Grant No. 2018058 from the United States–Israel Binational Science Foundation (BSF), Jerusalem, Israel. A. Z. is partially supported through a Fellowship from the Research Discovery Informatics Institute. The Flatiron Institute is a division of the Simons Foundation. Publisher Copyright: {\textcopyright} 2022 authors. Published by the American Physical Society.",
year = "2022",
month = oct,
doi = "10.1103/PhysRevX.12.041002",
language = "English (US)",
volume = "12",
journal = "Physical Review X",
issn = "2160-3308",
publisher = "American Physical Society",
number = "4",
}