  Graphene is a two-dimensional carbon material with a honeycomb lattice and
Dirac-type low-energy spectrum. In a strong magnetic field, where Coulomb
interactions dominate against disorder broadening, quantum Hall ferromagnetic
states realize at integer fillings. Extending the quantum Hall ferromagnetism
to the fractional filling case of massless Dirac fermions, we study the
elementally charge excitations which couple with the valley degrees of freedom
(so-called valley skyrmions). With the use of the density matrix renomalization
group (DMRG) method, the excitation gaps are calculated and extrapolated to the
thermodynamic limit. These results exhibit numerical evidences and criterions
of the skyrmion excitations in graphene.
