Effects of interactions in free-fermion hybrid entanglement transitions

Quantum hybrid dynamics, involving unitary gates and projective measurements, have been shown in a wide array of cases to exhibit a measurement-induced entanglement transition. These have been shown numerically to appear in bosonic and fermionic systems. While bosonic systems generally display an area-law to volume-law transition, a system with free fermion dynamics will tend to show an area-law to logarithmic-law transition, where entropy increases as the logarithm of the system size. In this work, we simulate a system where the unitary evolution consists mostly of free fermion unitary gates, but interspersed with interacting unitary gates, in an attempt to investigate a transition between logarithmic-law and volume-law phases.