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Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions.

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Measurement-induced phase transitions (MIPTs) in quantum systems reveal distinct universality classes. This study uses conformal field theory and numerical methods to differentiate these classes, finding unique scaling behaviors for different quantum systems.

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Area of Science:

  • Quantum Many-Body Physics
  • Quantum Information Theory
  • Condensed Matter Physics

Background:

  • Repeated local measurements can drive quantum many-body systems into a phase transition affecting their entanglement structure.
  • Existing studies on measurement-induced phase transitions (MIPTs) often show similar critical exponents, obscuring the number of distinct universality classes.
  • Understanding these universality classes is crucial for characterizing quantum system dynamics under measurement.

Purpose of the Study:

  • To investigate the properties of conformal field theories (CFTs) governing MIPTs.
  • To determine if generic and Clifford MIPTs belong to different universality classes.
  • To compare these MIPT universality classes with the percolation transition in qudits.

Main Methods:

  • Employed a numerical transfer-matrix method for analyzing (1+1)-dimensional quantum systems.
  • Extracted effective central charge and low-lying scaling dimensions of operators at critical points.
  • Utilized CFT techniques to probe the nature of MIPTs.

Main Results:

  • Provided evidence that generic and Clifford MIPTs for qubits reside in distinct universality classes.
  • Demonstrated that these MIPTs are different from the percolation transition for qudits (in the large on-site Hilbert space limit).
  • Observed multifractal scaling of correlation functions in the generic case, indicated by a continuous spectrum of scaling dimensions.

Conclusions:

  • The study successfully differentiates universality classes of MIPTs using CFT and numerical methods.
  • Results highlight the diversity of critical behaviors in quantum systems driven by measurements.
  • Findings contribute to a deeper understanding of quantum entanglement dynamics and critical phenomena.