Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions

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.