Collective excitations and the nature of Mott transition in undoped gapped graphene

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.