  The fermion disorder operator has been shown to reveal the entanglement
information in 1D Luttinger liquids and 2D free and interacting Fermi and
non-Fermi liquids emerging at quantum critical points(QCP). Here we study, by
means of large-scale quantum Monte Carlo simulation, the scaling behavior of
disorder operator in correlated Dirac systems. We first demonstrate the
logarithmic scaling behavior of the disorder operator at the Gross-Neveu (GN)
chiral Ising and Heisenberg QCPs, where consistent conformal field theory (CFT)
content of the GN-QCP in its coefficient is found. Then we study a 2D monopole
free deconfined quantum critical point (DQCP) realized between a quantum-spin
Hall insulator and a superconductor. Our data point to negative values of the
logarithmic coefficients such that the DQCP does not correspond to a unitary
CFT. Density matrix renormalization group calculations of the disorder operator
on a 1D DQCP model also detect emergent continuous symmetries.
