Universal properties of the measurement-induced phase transition with U(1) symmetry

Recently measurement-induced phase transitions have been studied in non-unitary quantum circuit evolving with a U(1) conserved charge. With increasing rate of measurements, the circuit exhibits a new type of charge-sharpening phase transition followed by the entanglement transition from a volume law to an area law phase. In this talk, we present a numerical study of the critical behavior of the entanglement transition and find it is described by a new universality class that is distinct from both the percolation transition and the Haar random circuit without a conservation law. We provide convincing numerical evidence based on computing the mutual information between two locally coupled Ancilla qubits in the same global charge sector and we estimate the bulk critical exponent. Further, emergent Lorentz invariance at the transition allows us to probe the properties of the underlying (1+1)d conformal field theory via its effective central charge (c_eff) and the leading scaling dimensions of the operators using a numerical transfer matrix method. Our numerical analysis predicts that both the bulk critical exponent and c_eff have much larger values than those of the percolation or random Haar circuit and thus uncover distinct signatures of global constraints in the dynamics on the measurement-induced criticality.