Operator scaling dimensions and multifractality at measurement-induced transitions

TL;DR

This study investigates the critical properties of measurement-induced phase transitions in quantum many-body systems, revealing different universality classes and multifractal scaling at the transition points through numerical analysis.

Contribution

It provides the first detailed numerical characterization of the conformal field theories governing measurement-induced phase transitions, distinguishing universality classes for different models.

Findings

Generic and Clifford MIPTs are in different universality classes.

Both MIPTs differ from percolation transition in large Hilbert space limit.

Evidence of multifractal scaling of correlation functions at criticality.

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 values of the critical exponents, making it unclear if there is only one underlying universality class. Here, we directly 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. 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 onsite 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.