Abstract:The construction of soluble lattice toy models is an important theoretical approach in the study of strongly interacting topological phases of matter. On the other hand, the primary experimental probe to such systems is via electromagnetic response. Somewhat unsatisfactorily, the current systematic construction of the lattice toy models focuses on braiding statistics and does not admit coupling to an electromagnetic background. Thus there is a mismatch between our theoretical approach and experimental probe. In this talk I introduce how to systematically incorporate electromagnetic response into the soluble lattice toy models, for a large class of abelian topological phases. [Reference: 1902.06756]