Generalized quantum measurements with matrix product states: Entanglement phase transition and clusterization

We propose a method, based on matrix product states, for studying the time evolution of many-body
quantum lattice systems under continuous and site-resolved measurement. Both the frequency and the strength of
generalized measurements can be varied within our scheme, thus allowing us to explore the corresponding two-
dimensional phase diagram. The method is applied to one-dimensional chains of nearest-neighbor interacting
hard-core bosons. A transition from an entangling to a disentangling (area-law) phase is found. However, by
resolving time-dependent density correlations in the monitored system, we find important differences between
different regions at the phase boundary. In particular, we observe a peculiar phenomenon of measurement-
induced particle clusterization that takes place only for frequent moderately strong measurements, but not for
strong infrequent measurements.