Measurement-induced quantum criticality under continuous monitoring

TLDR

The quantity of subsystem particle‑number fluctuations can be readily measured with quantum‑gas microscopy, offering a practical alternative to entanglement‑entropy measurements. The authors aim to characterize entanglement‑phase transitions from volume‑law to area‑law scaling under continuous position measurement and to propose an experimental test using particle‑number fluctuations. They employ a quantum‑trajectory framework to study continuous monitoring of a many‑body system and design a feasible experimental setup based on subsystem particle‑number fluctuations. The analysis reveals mutual‑information peaks that signal the transition, logarithmic entanglement scaling and algebraic scaling of physical observables at critical points, emergent conformal and Tomonaga‑Luttinger‑liquid–like spectral signatures in interacting one‑dimensional systems, and shows that such criticality is absent in noninteracting regimes and only appears in steady‑state conditional dynamics, not in unconditional Lindblad evolution.

Abstract

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. These intriguing critical phenomena are unique to steady-state regimes of the conditional dynamics at the single-trajectory level, and are absent in the unconditional dynamics obeying the Lindblad master equation, in which the system ends up with the featureless, infinite-temperature mixed state. We also propose a possible experimental setup to test the predicted entanglement transition based on the subsystem particle-number fluctuations. This quantity should readily be measured by the current techniques of quantum gas microscopy and is in practice easier to obtain than the entanglement entropy itself.