Volume-law to area-law entanglement transition in a non-unitary periodic Gaussian circuit

Abstract

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

5 pages, 2 figures, 6 pages of supplemental material. Updated Fig. 2 and added Ref. 29

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