System with Z₂ local gauge in the presence of U(1) global symmetry

Systems with local gauge symmetries host topological orders. Here we study a system with a local gauge symmetry supplemented by a global symmetry and its associated conserved charge. We investigate a generalization of Kitaev's toric code on a square lattice, which has both local Z2 gauge symmetry and global U(1) symmetry. Using quantum Monte Carlo simulation, we find that the system is gapped, and the ground state shows coexistence of symmetry breaking and topologically ordered phases. For different compactifications of the lattice, we find that the topological degeneracy changes. The microscopic details of the lattice arrangement affecting the topological degeneracy demonstrate a UV/IR mixing in this model.