Measurement-Induced Phase Transition in the Monitored Sachdev-Ye-Kitaev Model

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 SYK2 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.

Automated summary

In this study, Brownian SYK chains subjected to continuous monitoring were constructed to explore entanglement phase transitions. It was found that the entanglement transition is caused by symmetry breaking in the enlarged replica space, with a continuous O(2) symmetry between replicas in the noninteracting case leading to spontaneous breaking upon varying the measurement rate. The results suggest that the emergent replica criticality associated with the Goldstone mode leads to log-scaling entanglement entropy in the symmetry broken phase at low measurement rate, while area-law scaling is observed in the symmetric phase at higher measurement rate.