  We consider lattice deformations (both continuous and topological) in the
hexagonal lattice Hubbard model in the tight binding approximation to graphene,
involving operators with the range up to next-to-neighbor. In the low energy
limit, we find that these deformations give rise to couplings of the electronic
Dirac field to an external scalar (Yukawa) and gauge fields. The fields are
expressed in terms of original defects. As a by-product we establish that the
next-to-nearest order is the minimal range of deformations which produces the
complete gauge and scalar fields. We consider an example of Stone--Wales
defect, and find the associated gauge field.
