Ehud Altman
Quantum circuits consisting of random unitary gates and subject to local measurements have been shown to undergo a phase transition, tuned by the rate of measurement, from a state with volume-law entanglement to an area-law state. I will argue that a much richer phase structure emerges if symmetries are imposed on the circuit. However, the classification is governed by an enlarged effective symmetry, which combines the physical circuit symmetry with dynamical symmetries associated with the ensemble of quantum trajectories. This opens the door to of phases, which would not have been possible in presence of the circuit symmetry alone.
I will give two simple examples to illustrate these ideas: (i) a 1+1 dimensional circuit with Z2 spin symmetry gives rise to a number of phases including volume law states with distinct broken symmetries; (ii) A circuit with Gaussian fermion gates obeying only the Z2 fermion parity, nonetheless exhibits a critical phase separated from area law phases by a measurement induced Kosterlitz-Thouless transition.