▎ 摘　　要

The particle-hole continuum (PHC) for massive Dirac fermions provides an unprecedented opportunity for the formation of two collective split-off states, one in the singlet and the other in the triplet (spin-1) channel, when the short-range interactions are added to the undoped system. Both states are close in energy and are separated from the continuum of free particle-hole excitations by an energy scale of the order of the 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 composite boson, 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 the triplet mode at the Mott criticality is twice the velocity of the underlying Dirac fermions. The phase transition line in the space of U and Delta is in qualitative agreement with our previous dynamical mean field theory calculations.