  Quantum criticality, a manifestation of emergent scale invariance in electron
wavefunctions arises from intricate many-body quantum entanglement. One of the
natural venues for the criticality is clean undoped Dirac semimetals, known as
a marginally-renormalized critical phase. The ground state is only slightly
modified from the Slater-type product wavefunction because the scatterings from
weak disorder and Coulomb interactions are suppressed. Here, using the
renormalization group (RG) analysis, we show that a novel class of quantum
criticality appears in Dirac semimetals when the disorder strength becomes
sufficiently strong in the presence of Coulomb interactions so that a quantum
phase transition from the marginally-renormalized critical phase to a
disorder-dominated phase arises. The ground state at the critical point is a
quantum critical non-Fermi liquid (NFL), characterized by the properties of
strongly entangled low-energy states such as the absence of quasi-particles.
Near the critical point, unusually wide temperature regions with NFL behaviors
emerge.
