Phases of Gaussian fermionic circuits protected by hidden dynamical symmetries

Yimu Bao

Gaussian fermionic circuits consisting of unitary gates and local measurements that preserve the gaussianity of the wave function have been shown to undergo an entanglement phase transition tuned by the measurement rates. The subsystem entanglement entropy exhibits a critical scaling at moderate measurement rates and sharply changes to an area-law scaling when the rate is increased. In this talk, we show the physical circuit symmetry does not govern the phase transition on its own. Instead, it is extended by hidden dynamical symmetries to form an enlarged symmetry. In the circuits that only conserves fermion parity, we show an enlarged U(1) symmetry, which explains the U(1) critical phase and predicts a Kosterlitz-Thouless transition to an area-law phase. We examine our theoretical predictions via numerical simulations. We further discuss the enlarged symmetry in the circuits with physical U(1) symmetry and identify the relevant symmetry for the phase transition.