There are deep ties between lattice field theory and the physics of topological phases of materials. For example, the physics of quantum Hall effect and the corresponding chiral edge states have parallels in anomaly inflow of domain wall fermions on the lattice. Another striking example of this interrelation lies in the commonality between Chern insulators and abelian lattice gauge theories coupled to Wilson fermions. One of the research directions I am pursuing involves exploring the interrelations between lattice gauge theory and topological phases of terrestrial materials with the goal of facilitating a deeper understanding of lattice field theory and leading to designs of new quantum materials.