Geometric phases and competing orders in two dimensions

We discuss the problem of characterizing “quantum disordered” ground states, obtained upon loss of antiferromagnetic order on general lattices in two spatial dimensions, with arbitrary electronic band structure. A key result is the response in electron bilinears to the skyrmion density in the local antiferromagnetic order, induced by geometric phases. We also discuss the connection to topological terms obtained under situations where the electronic spectrum has a Dirac form.