SYK meets non-Hermiticity II: measurement-induced phase transition

TL;DR

This paper investigates measurement-induced entanglement phase transitions in Brownian SYK chains, revealing symmetry-breaking mechanisms and scaling behaviors in both noninteracting and interacting regimes through analytical and numerical methods.

Contribution

It introduces a large-$N$ analytical framework for SYK chains under measurement, identifying symmetry-breaking as the driver of entanglement transitions and characterizing the resulting phases.

Findings

Symmetry breaking causes entanglement phase transitions.

Log-scaling entanglement entropy in the symmetry-broken phase.

Area-law entanglement entropy in the symmetric phase.

Abstract

We construct Brownian Sachdev-Ye-Kitaev (SYK) chains subjected to continuous monitoring and explore possible entanglement phase transitions therein. We analytically derive the effective action in the large-$N$ limit and show that an entanglement transition is caused by the symmetry breaking in the enlarged replica space. In the noninteracting case with SYK$_2$ chains, the model features a continuous $O(2)$ symmetry between two replicas and a transition corresponding to spontaneous breaking of that symmetry upon varying the measurement rate. In the symmetry broken phase at low measurement rate, the emergent replica criticality associated with the Goldstone mode leads to a log-scaling entanglement entropy that can be attributed to the free energy of vortices. In the symmetric phase at higher measurement rate, the entanglement entropy obeys area-law scaling. In the interacting case, the continuous $O(2)$ symmetry is explicitly lowered to a discrete $C_4$ symmetry, giving rise to volume-law entanglement entropy in the symmetry-broken phase due to the enhanced linear free energy cost of domain walls compared to vortices. The interacting transition is described by $C_4$ symmetry breaking. We also verify the large-$N$ critical exponents by numerically solving the Schwinger-Dyson equation.