Period doubling in the two-dimensional antiferromagnet: Gauge fields and their anomalies

We construct an effective gauge-field theory model describing a two-dimensional quantum antiferromagnet in the flux-phase ground state. Due to period doubling the number of gauge fields is four rather than just one. These additional gauge fields correspond to lattice flux configurations in which the flux is staggered, which should be taken into account to enforce single occupancy within the magnetic unit cell. We calculate the corresponding quantum anomaly, present in such a model. In particular this leads to a generalized local flux hypothesis, which is tested numerically.