We consider a model of monitored quantum dynamics with quenched spatial randomness: specifically, random quantum circuits with spatially varying measurement rates. These circuits undergo a measurement-induced phase transition (MIPT) in their entanglement structure, but the nature of the critical point differs drastically from the case with constant measurement rate. In particular, at the critical measurement rate, we find that the entanglement of a subsystem of size ℓ scales as S∼ℓ√; moreover, the dynamical critical exponent z=∞. The MIPT is flanked by Griffiths phases with continuously varying dynamical exponents. We argue for this infinite-randomness scenario on general grounds and present numerical evidence that it captures some features of the universal critical properties of MIPT using large-scale simulations of Clifford circuits. These findings demonstrate that the relevance and irrelevance of perturbations to the MIPT can naturally be interpreted using a powerful heuristic known as the Harris criterion.

UR - https://arxiv.org/abs/2205.14002 ER - TY - JOUR T1 - Operator Scaling Dimensions and Multifractality at Measurement-Induced Transitions JF - Physical Review Letters Y1 - 2022 A1 - Aidan Zabalo A1 - Michael Gullans A1 - Justin H. Wilson A1 - Romain Vasseur A1 - Andreas W. W. Ludwig A1 - Sarang Gopalakrishnan A1 - David A. Huse A1 - J. H. Pixley AB -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.

VL - 128 UR - https://arxiv.org/abs/2107.03393 U5 - 10.1103/physrevlett.128.050602 ER -