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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 $U_c\approx 2.38 t$. 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.
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