Universal properties of the Abelian Higgs model and its quantum simulator with Rydberg-dressed interactions.

Analog quantum simulations of lattice gauge theory are a promising direction in understanding high energy physics. We derive a Hamiltonian formulation for the (1+1)-dimensional Abelian Higgs model that is manifestly gauge-invariant. The Hamiltonian formulation of the Polyakov loop can be obtained by the same method, which makes it possible to study this order parameter for the confinement/deconfinement phase transition experimentally. The corresponding quantum simulator is an asymmetric multi-leg ladder of atoms trapped in optical lattices and interacting with Rydberg-dressed interactions, where the required quadratic attractive interactions can be realized. The finite size scaling of the energy gap created by the insertion of a Polyakov loop can be obtained accurately by choosing spin truncations (the number of legs in the ladder) properly, which are cross-checked by tensor renormalization group calculations and Monte Carlo simulations. Phase transitions and quench dynamics also can be studied with this quantum simulator.