From Doubled Chern-Simons-Maxwell Lattice Gauge Theory to Extensions of the Toric Code

Understand

We regularize compact and non-compact Abelian Chern-Simons-Maxwell theories on a spatial lattice using the Hamiltonian formulation.

• We consider a doubled theory with gauge fields living on a lattice and its dual lattice.
• The Hilbert space of the theory is a product of local Hilbert spaces, each associated with a link and the corresponding dual link.
• The two electric field operators associated with the link-pair do not commute.