Entanglement Transition in a Monitored Free-Fermion Chain: From Extended Criticality to Area Law

We analyze the quantum trajectory dynamics of free fermions subject to continuous monitoring. For weak monitoring, we identify a novel dynamical regime of subextensive entanglement growth, reminiscent of a critical phase with an emergent conformal invariance. For strong monitoring, however, the dynamics favors a transition into a quantum Zeno-like area-law regime. Close to the critical point, we observe logarithmic finite size corrections, indicating a Berezinskii-Kosterlitz-Thouless mechanism underlying the transition. This uncovers an unconventional entanglement transition in an elementary, physically realistic model for weak continuous measurements. In addition, we demonstrate that the measurement aspect in the dynamics is crucial for whether or not a phase transition takes place.

Automated summary

This study analyzes the quantum trajectory dynamics of free fermions subject to continuous monitoring, revealing two distinct dynamical regimes for weak and strong monitoring, with the emergence of a quantum Zeno-like area-law regime under strong monitoring. The presence of logarithmic finite size corrections near the critical point suggests a Berezinskii-Kosterlitz-Thouless mechanism underlying the transition, highlighting the unconventional entanglement transition in a physically realistic model for weak continuous measurements. The crucial role of the measurement aspect in determining whether a phase transition occurs is also demonstrated.