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We discuss here how, when higher-order effects in the parameter$\frac{\ell}{\hbar} |\vec{p}|$, related to the lattice spacing $\ell$, areconsidered, pristine graphene, and other Dirac materials, can be used astabletop systems where generalized commutation relations are naturallyrealized. Such generalized algebras of quantization, which lead to generalizedversions of the Heisenberg uncertainty principle, are under intense scrutinythese days, as they could manifest a fundamental length scale of spacetime.Despite the efforts and the many intriguing results, there are no experimentalsignatures of any generalized uncertainty principle (GUP). Therefore, ourresults here, which tell how to use tabletop physical systems to test certainGUPs in analog experiments, should be of interest to practitioners of quantumgravity. We identify three different energy regimes that we call ``layers'',where the physics is still of a Dirac type but within precisely describedlimits. The higher the energy, the more sensitive the Dirac system becomes tothe effects of the lattice. Here such lattice plays the role of a discretespace where the Dirac quasi-particles live. With the goals just illustrated, wehad to identify the mapping between the high-energy coordinates, $X^i$, and thelow-energy ones, $x^i$, i.e., those measured in the lab. We then obtained threegeneralized Heisenberg algebras. For two of them we have the noticeable resultthat $X^i = x^i$, and for the third one we obtained an improvement with respectto an earlier work: the generalized coordinates expressed in terms of thestandard phase space variables, $X^i(x,p)$, and higher order terms.

Shadows of new physics on Dirac materials, analog GUPs and other amusements