Charge and Entanglement Criticality in a U(1)-Symmetric Hybrid Circuit of Qubits

Abstract

We study critical properties of the entanglement and charge-sharpening measurement-induced phase transitions in a non-unitary quantum circuit evolving with a U(1) conserved charge. Our numerical estimation of the critical properties of the entanglement transition at finite system sizes appears distinct from the generic non-conserving case and percolation. We provide two possible interpretations of this observation: (a) these two transitions occur at different measurement rates in the thermodynamic limit, but at finite system sizes their critical fans overlap and the critical exponents we probed here show a combination of both the criticality. Nonetheless, the multifractal properties of the entanglement transition remain distinct from the generic case without any symmetry, indicating a unique universality class due to the U(1) symmetry. (b) these two transitions occur at the same measurement rate at any length scale. Within this interpretation, our estimation of all the critical exponents are sharply different than the non-conserving case, again confirming the presence of a new universality class due U(1) symmetry. We compute entanglement critical exponents and correlation functions via various ancilla measures, use a transfer matrix for multifractality, and compute correlators associated with charge sharpening to explain these findings. Through these correlators, we also find evidence consistent with the charge-sharpening transition being of the Berezinskii-Kosterlitz-Thouless type (including the predicted ``jump'' in stiffness), which simultaneously argues for a broad critical fan for this transition. As a result, attempts to measure critical properties in this finite-size system will see anomalously large exponents predicted by our numerical analysis.

12+5 pages, 8+6 figures

References in corpus (18)

• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Random Quantum Circuits
• Critical properties of the measurement-induced transition in random quantum circuits
• Entanglement transition in a monitored free fermion chain -- from extended criticality to area law
• Observation of measurement-induced quantum phases in a trapped-ion quantum computer
• Measurement Protected Quantum Phases
• Measurement-induced entanglement and teleportation on a noisy quantum processor
• Experimental Realization of a Measurement-Induced Entanglement Phase Transition on a Superconducting Quantum Processor
• Conformal invariance and quantum non-locality in critical hybrid circuits
• Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
• Operator scaling dimensions and multifractality at measurement-induced transitions
• Symmetry enriched phases of quantum circuits
• Theory of free fermions under random projective measurements
• Critical phase and spin sharpening in SU(2)-symmetric monitored quantum circuits
• Charge fluctuation and charge-resolved entanglement in a monitored quantum circuit with $U(1)$ symmetry
• Simulating a measurement-induced phase transition for trapped ion circuits
• Exponential shortcut to measurement-induced entanglement phase transitions
• Boundary transfer matrix spectrum of measurement-induced transitions

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• Free-Fermion Dynamics with Measurements: Topological Classification and Adaptive Preparation of Topological States