Entanglement and Charge-Sharpening Transitions in U(1) Symmetric Monitored Quantum Circuits
By Utkarsh Agrawal, A. Zabalo, Kun Chen, Justin H. Wilson, Andrew C. Potter, J. Pixley, S. Gopalakrishnan, Romain Vasseur. Physical Review X, 2021
142 citations recorded by the source corpus.
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 disen-tangling 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 √ t in the absence of measurement, for even an infinitesimal rate of measurements, all average R´enyi 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. monitored quantum circuits. Our numerical results indicate that there are two distinct phases in the entangling (volume-law) regime p < p c , separated by a charge-sharpening critical point as p = p # . In the charge-fuzzy phase ( p < p # ), we identify three relevant time scales in the dynamics: For a large enough system, first (1) average R´enyi entropies crossover from diffusive [ S n> 1 ] ∼ √ t to ballistic ∼ t scaling over a time scale ∼ p − 3 / 2 , then (2) charge sharpens after the crossover time scale t # ∼ L , and finally (3) the system purifies over a much long time scale t π ∼ e L .
Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics
View Paper: https://www.semanticscholar.org/paper/3f03eb5ea269f5131edbe1ea69f1e99371400a4e
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In Atomic and Molecular Physics, and Optics
Citations in the corpus
- Random Quantum Circuits (2022, background): “When the discrete Ising symmetry is replaced by a continuous symmetry, such as a global U(1) symmetry, the phase structure appears to be even richer (267).”