  A Dirac fermion emerges as a result of interplay between symmetry and
topology in condensed matter. Current research moves towards investigating the
Dirac fermions in the presence of manybody effects in correlated system. Here,
we demonstrate the emergence of correlation-induced symmetry-protected Dirac
semimetal state in the lightly-doped spin-orbit-coupled Mott insulator
Sr$_2$IrO$_4$. We find that the nonsymmorphic crystalline symmetry stabilizes a
Dirac line-node semimetal and that the correlation-induced symmetry-breaking
electronic order further leads to a phase transition from the Dirac line-node
to a Dirac point-node semimetal. The latter state is experimentally confirmed
by angle-resolved photoemission spectroscopy and terahertz spectroscopy on
Sr$_2$(Ir,Tb)O$_4$ and (Sr,La)$_2$IrO$_4$. Remarkably, the electrodynamics of
the massless Dirac carriers is governed by the extremely small scattering rate
of about 6 cm$^{-1}$ even at room temperature, which is iconic behavior of
relativistic quasiparticles. Temperature-dependent changes in electrodynamic
parameters are also consistently explained based on the Dirac point-node
semimetal state.
