Lattice gauge theory treatment of strongly correlated Dirac semimetals

We observe the effect of Coulomb interaction in three-dimensional Dirac semimetals in the strong-coupling limit. Model of the system is constructed in terms of lattice gauge theory, with the Coulomb interaction mediated by U(1) gauge field defined on the lattice. We improve the formulation by introducing a field of positive background charge, and extrapolate our analysis to the "continuous-Time" limit, where the lattice spacing in the imaginary-Time direction reaches zero. We find that the system in the strong-coupling limit reduces to a strongly coupled repulsive Hubbard model, which favors charge neutrality for each lattice site, turning the system into a Mott insulator. We also evaluate the discretization error, to give a proper understanding of the effective model obtained by strong-coupling expansion.