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We consider a system of neutral, bosonic atoms on a square lattice subject to an artificial magnetic field. We focus on a field strength of half a Dirac flux quantum through every plaquette, which implies two minima in the lower single particle band. For repulsive interactions, we show that the many particle ground state possesses both superfluid and orbital antiferromagnetic order. For attractive interactions, we find a fragmented Bose--Einstein condensate without net orbital currents. |
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