Phase transition in von Neumann entropy from replica symmetry breaking
Shao-Kai Jian (Department of Physics and Engineering Physics, Tulane University, New Orleans, Louisiana, 70118, USA); Brian Swingle (Department of Physics, Brandeis University, Waltham, Massachusetts, 02453, USA)
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 → 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.
