Sebastian DIEHL
A wave function exposed to measurements undergoes pure state dynamics, with deterministic unitary and probabilistic measurement induced state updates, defining a quantum trajectory. For many-particle systems, the competition of these different elements of dynamics can give rise to a scenario similar to quantum phase transitions, in the ensemble of quantum trajectories.
Here we study such transitions in various continuously monitored fermion systems. We establish novel types of transitions characterized by distinct scaling or the entanglement entropy, interpolating between regimes of logarithmic, area law, and sub-volume algebraic growth. The numerical findings are explained in terms of a replica Keldysh field theory, identifying the relevant degrees of freedom stabilizing the phases, and driving the phase transitions. Beyond the stationary states of such systems, we also explore the dynamics of purification of chaotic many-body systems set in competition with measurements.