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 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 Renyi entropies grow sub-ballistically as root t in the absence of measurement, for even an infinitesimal rate of measurements, all average Renyi entropies grow ballistically with time similar to 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.

Automated summary

The study investigates the enrichment of entanglement dynamics in nonunitary quantum circuits and reveals a charge-sharpening transition and an entanglement transition. The presence of measurements causes all average Renyi entropies to grow ballistically with time.