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Operator scaling dimensions and multifractality at measurement-induced transitions



Michael Gullans, Zabalo Aidan, Justin Wilson, Romain Vasseur, Andreas Ludwig, Sarang Gopalakrishnan Gopalakrishnan, David Huse, Jed Pixley


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.
Physical Review Letters


Disordered systems, statistical mechanics, quantum physics


Gullans, M. , Aidan, Z. , Wilson, J. , Vasseur, R. , Ludwig, A. , Gopalakrishnan, S. , Huse, D. and Pixley, J. (2022), Operator scaling dimensions and multifractality at measurement-induced transitions, Physical Review Letters, [online],, (Accessed April 18, 2024)
Created February 3, 2022, Updated November 29, 2022