Volume-Law to Area-Law Entanglement Transition in a Nonunitary Periodic Gaussian Circuit

We consider Gaussian quantum circuits that alternate unitary gates and postselected weak measurements, with spatial translation symmetry and time p eriodicity. We show analytically that such models can host different kinds of measurement-induced phase transitions detected by entanglement entropy, by mapping the unitary gates and weak measurements onto Möbius transformations. We demonstrate the existence of a log-law to area-law transition, as well as a volume-law to area-law transition at a finite measurement amplitude. For the latter, we compute the critical exponent ν for the Hartley, von Neumann and Rényi entropies exactly.