Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits

• URL: http://arxiv.org/abs/2107.10279v2
• Date: Tue, 4 Oct 2022 15:47:43 GMT
• Title: Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• Authors: Utkarsh Agrawal, Aidan Zabalo, Kun Chen, Justin H. Wilson, Andrew C. Potter, J. H. Pixley, Sarang Gopalakrishnan, and Romain Vasseur
• Abstract summary: We study how entanglement dynamics in non-unitary quantum circuits can be enriched in the presence of charge conservation. We uncover a charge-sharpening transition that separates different scrambling phases with volume-law scaling of entanglement. We find that while R'enyi entropies grow sub-ballistically as $sqrttt$ in the absence of measurement, for even an infinitesimal rate of measurements, all average R'enyi entropies grow ballistically with time.
• Score: 1.1968749490556412
• License: http://creativecommons.org/licenses/by/4.0/
• 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 non-unitary 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\'enyi entropies grow sub-ballistically as $\sqrt{t}$ in the absence of measurement, for even an infinitesimal rate of measurements, all average R\'enyi entropies grow ballistically with time $\sim t$. 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.

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