  We study the Mott transition in a two-dimensional lattice spinless fermion
model with nearest neighbors density-density interactions. By means of a
two-dimensional Jordan-Wigner transformation, the model is mapped onto the
lattice XXZ spin model, which is shown to possess a Quantum Group symmetry as a
consequence of a recently found solution of the Zamolodchikov Tetrahedron
Equation. A projection (from three to two space-time dimensions) property of
the solution is used to identify the symmetry of the model at the Mott critical
point as U_q(sl(2))xU_q(sl(2)), with deformation parameter q=-1. Based on this
result, the low-energy Effective Field theory for the model is obtained and
shown to be a lattice double Chern-Simons theory with coupling constant k=1
(with the standard normalization). By further employing the Effective Filed
Theory methods, we show that the Mott transition that arises is of topological
nature, with vortices in an antiferromagnetic array and matter currents
characterized by a d-density wave order parameter. We also analyze the behavior
of the system upon weak coupling, and conclude that it undergoes a quantum
gas-liquid transition which belongs to the Ising universality class.
