  Topological quantum phase transitions intrinsically intertwine
self-similarity and topology of many-electron wave-functions, and divining them
is one of the most significant ways to advance understanding in condensed
matter physics. Our focus is to investigate an unconventional class of the
transitions between insulators and Dirac semimetals whose description is beyond
conventional pseudo relativistic Dirac Hamiltonian. At the transition without
the long-range Coulomb interaction, the electronic energy dispersion along one
direction behaves like a relativistic particle, linear in momentum, but along
the other direction it behaves like a non-relativistic particle, quadratic in
momentum. Various physical systems ranging from TiO${}_2$-VO${}_2$
heterostructure to organic material $\alpha$-(BEDT-TTF)${}_2$ I${}_3$ under
pressure have been proposed to have such anisotropic dispersion relation. Here,
we discover a novel quantum criticality at the phase transition by
incorporating the 1/r long-range Coulomb interaction. Unique interplay between
the Coulomb interaction and electronic critical modes enforces not only the
anisotropic renormalization of the Coulomb interaction but also marginally
modified electronic excitation. In connection with experiments, we investigate
several striking effects in physical observables of our novel criticality.
