  Particle-hole continuum (PHC) for massive Dirac fermions in presence of short
range interactions, provides an unprecedented opportunity for formation of two
collective split-off states, one in the singlet and the other in the triplet
(spin-1) channel in undoped system. Both poles are close in energy and are
separated from thec continuum of free particle-hole excitations by an energy
scale of the order of gap parameter $\Delta$. They both disperse linearly with
two different velocities reminiscent of spin-charge separation in Luttinger
liquids. When the strength of Hubbard interactions is stronger than a critical
value, the velocity of singlet excitation which we interpret as a charge boson
composite becomes zero, and renders the system a Mott insulator. Beyond this
critical point, the low-energy sector is left with a linearly dispersing
triplet mode -- a characteristic of a Mott insulator. The velocity of triplet
mode at the Mott criticality is twice the velocity of underlying Dirac
fermions. The phase transition line in the space of $U$ and $\Delta$ is in
qualitative agreement with a more involved dynamical mean field theory (DMFT)
calculation.
