Phase transition in von Neumann entanglement entropy from replica symmetry breaking

TL;DR

This paper investigates how monitored Brownian SYK chains exhibit a phase transition in entanglement entropy from volume-law to area-law, driven by measurement rate and linked to replica symmetry breaking.

Contribution

It introduces an analytical framework for understanding the entanglement transition in monitored SYK chains, highlighting the role of replica symmetry breaking in the phase change.

Findings

Entanglement entropy transitions from volume-law to area-law with increased monitoring.

The transition point corresponds to replica symmetry unbreaking.

Analytical continuation of R{é}nyi entropy reveals the phase transition mechanism.

Abstract

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