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We study the promising idea of using dipolar molecular systems as analog quantum simulators for quantum link models, which are discrete versions of lattice gauge theories. In a quantum link model the link variables have a finite number of degrees of freedom and discrete values. We construct the effective Hamiltonian of a system of dipolar molecules with electric dipole-dipole interactions, where we use the tunable parameters of the system to match it to the target Hamiltonian describing a U(1) quantum link model in 1+1 dimensions.

$(1+1)$-d $U(1)$ Quantum Link Models from Effective Hamiltonians of Dipolar Molecules