Fluctuation as a probe of entanglement transition in a monitored free-fermion chain
Phys. Rev. A 112, 012604 – Published 7 July, 2025
DOI: https://doi.org/10.1103/ps1h-ftfw
Abstract
We investigate the measurement-induced entanglement transition (MIET) in a free-fermion chain under continuous measurements, using fluctuation as a scalable and accessible probe. The bipartite fluctuation of particle number within the subsystem is demonstrated to exhibit behaviors analogous to that of entanglement entropy. It effectively captures the nonequilibrium entanglement dynamics, as well as the transition in steady states from the critical phase with subextensive growth law to the area-law phase. By performing finite-size scaling analysis, we identify the critical measurement strength and demonstrate that the fluctuation can serve as a reliable indicator of the MIET. The results are consistent with previous entanglement entropy studies and reveal that the MIET belongs to the Berezinskii-Kosterlitz-Thouless universality class. Even when there are long-range hoppings or disorders, the fluctuation still acts as a reliable probe for the MIET. This approach offers a practical alternative to directly measuring entanglement entropy in monitored free-fermion chains, particularly for larger systems.
