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Due to effective enhancement of the Coulomb coupling strength in thevacuum-suspended graphene, the system may turn from a semimetal into aninsulator by the formation of a gap in the fermionic spectrum. This phenomenonis analogous to the spontaneous breaking of chiral symmetry in thestrong-coupling relativistic field theories. We study this "chiral symmetrybreaking" and associated collective excitations on graphene in the strongcoupling regime by taking U(1) lattice gauge theory as an effective model forgraphene. Both compact and non-compact formulations of the U(1) gauge actionshow chiral symmetry breaking with equal magnitude of the chiral condensate(exciton condensate) in the strong coupling limit, while they start to deviatefrom the next-to-leading order in the strong coupling expansion. Phase andamplitude fluctuations of the order parameter are also investigated: inparticular, a mass formula for the pseudo-Nambu--Goldstone mode($\pi$-exciton), which is analogous to Gell-Mann--Oakes--Renner relation forthe pion in quantum chromodynamics (QCD), is derived from the axialWard-Takahashi identity. To check the applicability of the effective fieldtheory description, typical energy scales of fermionic and bosonic excitationsare estimated by identifying the lattice spacing of the U(1) gauge theory withthat of the original honeycomb lattice of graphene.

Chiral Symmetry Breaking in Monolayer Graphene by Strong Coupling Expansion of Compact and Non-compact U(1) Lattice Gauge Theories