Entanglement negativity at the critical point of measurement-driven transition

Abstract: We study the entanglement behavior of a random unitary circuit punctuated by projective measurements at the measurement-driven phase transition in one spatial dimension. We numerically study the logarithmic entanglement negativity of two disjoint intervals and find that it scales as a power of the cross-ratio. We investigate two systems: (1) Clifford circuits with projective measurements, and (2) Haar random local unitary circuit with projective measurements. Remarkably, we identify a power-law behavior of entanglement negativity at the critical point. Previous results of entanglement entropy and mutual information point to an emergent conformal invariance of the measurement-driven transition. Our result suggests that the critical behavior of the measurement-driven transition is distinct from the ground state behavior of any \emph{unitary} conformal field theory.