Understand
We investigate entanglement phase transitions from volume-law to area-law entanglement in a quantum many-body state under continuous position measurement on the basis of the quantum trajectory approach.
- We find the signatures of the transitions as peak structures in the mutual information as a function of measurement strength, as previously reported for random unitary circuits with projective measurements.
- At the transition points, the entanglement entropy scales logarithmically and various physical quantities scale algebraically, implying emergent conformal criticality, for both integrable and nonintegrable one-dimensional interacting Hamiltonians; however, such transitions have been argued to be absent in noninteracting regimes in some previous studies.
- With the aid of $U(1)$ symmetry in our model, the measurement-induced criticality exhibits a spectral signature resembling a Tomonaga-Luttinger liquid theory from symmetry-resolved entanglement.