Strong-coupling approach to Mott transition of massless and massive Dirac fermions on honeycomb lattice

Phase transitions in the Hubbard model and ionic Hubbard model at half-filling on the honeycomb lattice are investigated in the strong-coupling perturbation theory which corresponds to an expansion in powers of the hopping t around the atomic limit. Within this formulation we find analytic expressions for the single-particle spectrum, whereby the calculation of the insulating gap is reduced to a simple root finding problem. This enables high-precision determination of the insulating gap that does not require any extrapolation procedure. The critical value of Mott transition on the honeycomb lattice is obtained to be U-c approximate to 2.38t. Studying the ionic Hubbard model at the lowest order, we find two insulating states, one with Mott character at large U and another with single-particle gap character at large ionic potential Delta. The present approach gives a critical gapless state at U = 2 Delta at lowest order. By systematically improving on the perturbation expansion, the density of states around this critical gapless phase reduces.