  We show that graphene, in its simplest form and settings, is a practical
table-top realization of the analog of exotic quantum gravity scenarios, which
are speculated to lead to certain generalized Heisenberg algebras. In
particular, we identify three different energy regimes (the ``layers'') where
the physics is still of a pseudorelativistic (Dirac) type but more and more
sensitive to the effects of the lattice. This plays here a role analog to that
of a discrete space, where the Dirac quasiparticles live. This work improves
and pushes further earlier results, where the physical meaning of the high
energy momenta was clear, but the conjugate coordinates only had a purely
abstract description. Here we find the physical meaning of the latter by
identifying the mapping between the high-energy coordinates and low-energy
ones, i.e., those measured in the lab. We then obtain two generalized
Heisenberg algebras that were not noticed earlier. In these two cases, we have
the striking result that the high-energy coordinates just coincide with the
standard ones, measured in the lab. A third generalized Heisenberg algebra is
obtained, and it is an improvement of the results obtained earlier in two
respects: we now have an expression of the generalized coordinates in terms of
the standard phase-space variables, and we obtain higher order terms. All
mentioned results clearly open the doors to table-top experimental
verifications of many generalized uncertainty principle-corrected predictions
of the quantum gravity phenomenology.
