Phase transition in von Neumann entanglement entropy from replica symmetry breaking

Shao-Kai Jian; Brian Swingle

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arXiv · 2108.11973

Phase transition in von Neumann entanglement entropy from replica symmetry breaking

Shao-Kai Jian·Brian Swingle

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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.

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quant-ph cond-mat.stat-mech cond-mat.str-el hep-th

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Shao-Kai Jian, Brian Swingle. 2021-08-26. Phase transition in von Neumann entanglement entropy from replica symmetry breaking. https://arxiv.org/abs/2108.11973

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