  Currently, there is much interest in discovering analytically tractable
(3+1)-dimensional models that describe interacting fermions with emerging
topological properties. Towards that end we present a three-dimensional
tight-binding model of spinless interacting fermions that reproduces, in the
low energy limit, a (3+1)-dimensional Abelian topological quantum field theory
called BF model. By employing a mechanism equivalent to the Haldane's Chern
insulator, we can turn the non-interacting model into a three-dimensional
chiral topological insulator. We then isolate energetically one of the two
Fermi points of the lattice model. In the presence of suitable fermionic
interactions, the system, in the continuum limit, is equivalent to a
generalised (3+1)-dimensional Thirring model. The low energy limit of this
model is faithfully described by the BF theory. Our approach directly
establishes the presence of (2+1)-dimensional BF theory at the boundary of the
lattice and it provides a way to detect the topological order of the model
through fermionic density measurements.

Strongly Correlated Electrons