  Motivated by recent experimental and calculational investigations of bilayer,
hydrogenated and fluorinated graphene, we apply the formalisms of U(1) QED
(quantum electrodynamics) and SU(2) QCD (quantum chromodynamics) theories of
strongly correlated state. Unlike non-bipartite triangular lattice, on
bipartite honeycomb lattice there always exists a monopole that transforms
trivially under all the microscopic symmetries, destabilizing the Dirac spin
liquid (DSL), so that one can continuously tune the DSL state to the state with
parent SU(2) instead of U(1) gauge group. The SU(2) theory describes a
spin-liquid state which is different from usual DSL and is probably unstable
with respect to Neel or valence-bond solid (VBS) phases, except for the quantum
critical point. This point of view means a possibility of VBS states in
graphene systems.
