Abstract: We derive an effective spin Hamiltonian for the (1 + 1)-dimensional Abelian Higgs model (scalar QED) in the strongly coupled region by integrating out the link variables. With finite spin truncations, the Hamiltonian can be matched with a 1-dimensional two-species Bose Hubbard model in the strong-coupling limit that can be implemented with cold atoms on an optical lattice. By performing Monte Carlo simulations and Tensor Renormalization Group methods to the original Abelian Higgs model, and applying DMRG to the effective quantum Hamiltonian, we show that they share similar behaviors. This method can be easily extended to study more complecated models like the sQED with topological charges, Polyakov loops and higher dimensional models. We discuss practical experimental implementations for our quantum simulator. We emphasize that this proposal for quantum simulating a gauge theory uses a manifestly gauge-invariant formulation and Gauss's Law is therefore automatically satisfied.
