Measurement induced phase transitions in free-fermionic quantum circuits

The advent of quantum simulation platforms has motivated the study of new theoretical "quantum circuit" models for the dynamics of quantum many-body systems. In recent years, these models have revealed new many-body phenomena of physical interest. A particularly important example is that of the so-called measurement induced phase transitions. In this context, we will study systems that evolve through a unitary circuit, which generates quantum entanglement, interspersed with local projective measurements, which instead tend to destroy it. By increasing the frequency of these measurements, a transition between two phases is observed, in which the entanglement passes from a "volume-law" to an "area-law". The goal of this thesis is to study circuit dynamics that can be mapped onto non-interacting fermions. In this context, recent studies have demonstrated the absence of a phase transition. The objective of the thesis is to investigate whether changes to the standard measurement protocol can lead to the appearance of a transition.