Phase transition in von Neumann entanglement entropy from replica symmetry breaking

Abstract

We study the entanglement transition in monitored Brownian SYK chains in the large-$N$ limit. Without measurement the steady state $n$-th Rényi entropy is obtained by summing over a class of solutions, and is found to saturate to the Page value in the $n\to 1$ limit. In the presence of measurements, the analytical continuation $n\to 1$ is performed using the cyclic symmetric solution. The result shows that as the monitoring rate increases, a continuous von Neumann entanglement entropy transition from volume-law to area-law occurs at the point of replica symmetry unbreaking.

arXiv comment33 pages, 3 figures

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