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Measurement-induced entanglement phase transitions, caused by the competition between entangling unitary dynamics and disentangling projective measurements, have been studied in various random circuit models in recent years. In this paper, we study the dynamics of averaged purity for a simple N-qudit Brownian circuit model with all-to-all random interaction and measurements. In the large-N limit, our model is mapped to a one-dimensional quantum chain in the semi-classical limit, which allows us to analytically study critical behaviors and various other properties of the model. We show that there are two phases distinguished by the behavior of the total system entropy in the long time. In addition, the two phases also have distinct subsystem entropy behavior. The low measurement rate phase has a first-derivative discontinuity in the behavior of second Renyi entropy versus subsystem size, similar to the "Page curve" of a random state, while the other phase has a smooth entropy curve. About the speaker: Xiao-Liang Qi finished his Ph. D. at the Institute for Advanced Study, Tsinghua University in 2007. He did postdoctoral research at Stanford University and UC Santa Barbara, and joined the faculty of Stanford University in 2010. In recent years, he has been mainly working on the relation of quantum information, quantum gravity and quantum many-body physics. He has also worked on topological states of matter and strongly correlated systems. |
