Measurement-induced criticality in monitored quantum circuits with U(1) symmetry

The entanglement entropy shows a phase transition from a volume-law phase to an area-law phase, called measurement-induced entanglement transition, when a pure quantum state evolved under unitary dynamics is subject to local projective measurements. It is intensively studied due to emergence of conformal invariance at the phase transition, which is rarely found in non-equilibrium systems. In this talk, I will discuss critical phenomena in unitary-projective hybrid quantum circuits with U(1) symmetry (charge conservation). Numerical results show that, in addition to the conventional entanglement transition, a new transition obeying the Tomonaga-Luttinger liquid theory appears. The latter transition is characterized by critical behaviors in a subsystem charge fluctuation, a charge correlator, and the entanglement resolved by conserved charges. I also show that a correlator of subsystem charges can be used to locate this new transition point.