  We introduce a model of Dirac fermions in 2+1 dimensions with a semimetallic,
a quantum spin-Hall insulating (QSHI), and an s-wave superconducting (SSC)
phase. The phase diagram features a multicritical point at which all three
phases meet as well as a QSHI-SSC deconfined critical point. The QSHI and SSC
orders correspond to mutually anti-commuting mass terms of the Dirac
Hamiltonian. Based on this algebraic property, SO(5) symmetric field theories
have been put forward to describe both types of critical points. Using quantum
Monte Carlo simulations, we directly study the operator that rotates between
QSHI and SSC states. The results suggest that it commutes with the low-energy
effective Hamiltonian at criticality but has a gap in the ordered phases. This
implies an emergent SO(5) symmetry at both the multicritical and the deconfined
critical points.
