Charge and entanglement criticality in a U(1)-symmetric hybrid circuit of qubits

TY - JOUR

T1 - Charge and entanglement criticality in a U(1)-symmetric hybrid circuit of qubits

AU - Chakraborty, Ahana

AU - Chen, Kun

AU - Zabalo, Aidan

AU - Wilson, Justin H.

AU - Pixley, J. H.

N1 - Publisher Copyright: © 2024 American Physical Society.

PY - 2024/7/15

Y1 - 2024/7/15

N2 - We study critical properties of the entanglement and charge-sharpening measurement-induced phase transitions in a nonunitary 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 nonconserving 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 criticalities. 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 lengthscale. Within this interpretation, our estimation of all the critical exponents is sharply different from the nonconserving case, again confirming the presence of a new universality class due to U(1) symmetry. We compute entanglement critical exponents and correlation functions via various ancilla measures, we use a transfer matrix for multifractality, and we 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.

AB - We study critical properties of the entanglement and charge-sharpening measurement-induced phase transitions in a nonunitary 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 nonconserving 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 criticalities. 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 lengthscale. Within this interpretation, our estimation of all the critical exponents is sharply different from the nonconserving case, again confirming the presence of a new universality class due to U(1) symmetry. We compute entanglement critical exponents and correlation functions via various ancilla measures, we use a transfer matrix for multifractality, and we 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.

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U2 - 10.1103/PhysRevB.110.045135

DO - 10.1103/PhysRevB.110.045135

M3 - Article

SN - 2469-9950

VL - 110

JO - Physical Review B

JF - Physical Review B

IS - 4

M1 - 045135

ER -