Measurement-induced dynamics of many-body systems at quantum criticality

We consider a dynamic protocol for quantum many-body systems, which enables us to study the interplay between unitary Hamiltonian driving and random local projective measurements. While the unitary dynamics tends to increase entanglement, local measurements tend to disentangle, thus favoring decoherence. The competition of the two drivings is analyzed at quantum transitions, where the presence of critical correlations substantially changes the impact of local measurements. We identify a particular regime (dynamic scaling limit) within a dynamic scaling framework, where the two mechanisms develop a nontrivial interplay and peculiar scaling behaviors. This is supported by a numerical analysis of a measurement-driven quantum Ising chain. The local measurement process generally tends to suppress quantum correlations, even in the dynamic scaling limit. The power law of the decay of the quantum correlations turns out to be enhanced at the quantum transition.