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The effective U(1)-Higgs theory at strong coupling on optical lattices?

We discuss the U(1)-Higgs model in two dimensions in the strongly coupled regime. If we neglect the plaquette interactions, we generate an effective theory where link variables are integrated out, producing 4-field operators. Plaquette interactions can be restored order by order as in recent calculations with staggered fermions. In the case of a SU(2) gauge theory with fermions, this strong coupling expansion can be related to the strong coupling expansion of Fermi-Hubbard models possibly implementable on optical lattice. We would like to provide a similar construction relating the U(1)-Higgs model to some Bose-Hubbard model. As a first step in this direction, we discuss a recent proposal to implement the O(2) model on optical lattices using a 87Rb and 41K Bose-Bose mixture of cold atoms.