Entanglement negativity at the critical point of measurement-driven transition

TL;DR

This paper investigates the critical behavior of entanglement negativity in measurement-driven phase transitions within 1D random unitary circuits, revealing a power-law scaling and suggesting a distinct critical universality from known conformal field theories.

Contribution

It provides the first numerical evidence of power-law entanglement negativity at the transition, indicating a new universality class different from ground state conformal field theories.

Findings

Entanglement negativity scales as a power of the cross-ratio at criticality.

Measurement-driven transition exhibits emergent conformal invariance.

Critical behavior differs from that of known unitary conformal field theories.

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.