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Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions

A. Zabalo, M. J. Gullans, J. H. Wilson, R. Vasseur, A. W. W. Ludwig, S. Gopalakrishnan, David A. Huse, and J. H. Pixley
Phys. Rev. Lett. 128, 050602 – Published 3 February 2022
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Abstract

Repeated local measurements of quantum many-body systems can induce a phase transition in their entanglement structure. These measurement-induced phase transitions (MIPTs) have been studied for various types of dynamics, yet most cases yield quantitatively similar critical exponents, making it unclear how many distinct universality classes are present. Here, we probe the properties of the conformal field theories governing these MIPTs using a numerical transfer-matrix method, which allows us to extract the effective central charge, as well as the first few low-lying scaling dimensions of operators at these critical points for (1+1)-dimensional systems. Our results provide convincing evidence that the generic and Clifford MIPTs for qubits lie in different universality classes and that both are distinct from the percolation transition for qudits in the limit of large on-site Hilbert space dimension. For the generic case, we find strong evidence of multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

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  • Received 30 July 2021
  • Accepted 5 January 2022

DOI:https://doi.org/10.1103/PhysRevLett.128.050602

© 2022 American Physical Society

Physics Subject Headings (PhySH)

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied PhysicsStatistical Physics & Thermodynamics

Authors & Affiliations

A. Zabalo1, M. J. Gullans2,3, J. H. Wilson1,4,5, R. Vasseur6, A. W. W. Ludwig7, S. Gopalakrishnan8,9, David A. Huse2, and J. H. Pixley1,2,10

  • 1Department of Physics and Astronomy, Center for Materials Theory, Rutgers University, Piscataway, New Jersey 08854, USA
  • 2Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
  • 3Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
  • 4Department of Physics and Astronomy, Louisiana State University, Baton Rouge, Louisiana 70803, USA
  • 5Center for Computation and Technology, Louisiana State University, Baton Rouge, Louisiana 70803, USA
  • 6Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA
  • 7Department of Physics, University of California, Santa Barbara, California 93106, USA
  • 8Department of Physics, The Pennsylvania State University, University Park, Pennsylvania 16802, USA
  • 9Department of Physics and Astronomy, CUNY College of Staten Island, Staten Island, New York 10314, USA
  • 10Center for Computational Quantum Physics, Flatiron Institute, 162 5th Avenue, New York, New York 10010, USA

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Issue

Vol. 128, Iss. 5 — 4 February 2022

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