Free-Fermion Measurement-Induced Volume- to Area-Law Entanglement Transition in the Presence of Fermion Interactions

At a volume- to area-law entanglement transition in a quantum many-body system, quantum chaos is arrested. We argue that this tends to make a certain "mass" term, which reflects the presence of interactions in the field-theory description, vanish at the measurement-induced phase transition (MIPT). To support this idea, we consider the generic MIPT possessing no conserved quantities that describes 1D monitored, interacting Majorana fermions in Altland-Zirnbauer symmetry class DIII, subjected to fermion-parity measurements and unitary evolution. In this case, we predict a non-interacting critical theory at the MIPT; the volume-law phase arises through the dangerously irrelevant "mass." We propose several possible future numerical tests of our conjecture. In addition, we identify an analytically controlled candidate non-interacting MIPT critical point in symmetry class DIII at which the interactions are dangerously RG-irrelevant.