Late time von Neumann entropy and its transition

We study the late-time entanglement entropy and its transition in monitored Brownian SYK chains in the large-N limit. Without measurement the steady state n-th Renyi entropy is obtained by summing over a class of solutions, and is found to saturate to the Page value in the n=1 limit. In the presence of measurements, the analytical continuation n=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.