Universal correlations in quantum trajectories of the transverse field Ising model

While the universal properties of quantum systems near a critical point are well understood in equilibrium, determining robust signatures of quantum criticality in nonequilibrium systems remains an ongoing challenge. Motivated by recent works on measurement-induced dynamical phase transitions in quantum circuits, we investigate the effect of repeated measurements of an edge spin in a transverse field Ising spin chain, which is initialized in its ground state and tuned across the quantum critical point. While the continuous monitoring drives the system out of equilibrium and destroys criticality in traditional observables obtained from the averaged density matrix, we find that signatures of quantum critical behavior can nevertheless be seen in individual measurement trajectories of the system. Using a combination of numerical simulations and field-theoretic techniques, we identify observables nonlinear in the density matrix, which remain sensitive to universal CFT behavior in the nonequilibrium monitored system. This work provides a step towards exploring critical behavior in monitored systems accessible to experiments.