Description
We investigate the entanglement structure and wave function characteristics of continuously monitored free fermions with $U(1)$-symmetry in 2D. Using exact numerical simulations, we establish the phenomenology of the entanglement transition and explore the similarities and differences with Anderson-type localization transitions. At weak monitoring, we observe characteristic $L\log(L)$ entanglement growth and multifractal dimension $D_q=2$, resembling a metallic Fermi liquid. At strong monitoring, we find a phase transition into an area law, localized phase and a Poissonian distribution for the entanglement spectrum is seen. In between, we reveal another point in the low-measurement regime with indications of an emergent conformal invariance and strong multifractality. Furthermore, we find another witness of multifractality in the spectral form factor. Our results shape the understanding of a monitoring-induced metal-to-insulator transition in entanglement content. This establishes 2D monitored fermions as a unique platform to explore the connection between non-unitary quantum dynamics in $D$ dimensions and quantum statistical mechanics in $D+1$ dimensions.
References
K. Chahine, M. Buchhold , "Entanglement phases, localization and multifractality of monitored free fermions in two dimensions", arXiv:2309.12391 (2023)
