Geometric phases and the magnetization process in quantum antiferromagnets

The physics underlying the magnetization process of quantum antiferromagnets is revisited from the viewpoint of geometric phases. A continuum variant of the Lieb-Schultz-Mattis-type approach to the problem is put forth, where the commensurability condition of Oshikawa et al. () derives from a Berry connection formulation of the system’s crystal momentum. We then go on to formulate an effective field theory which can deal with higher dimensional cases as well. We find that a topological term, whose principle function is to assign Berry phase factors to space-time vortex objects, ultimately controls the magnetic behavior of the system. We further show how our effective action maps into a Z₂ gauge theory under certain conditions, which in turn allows for the occurrence of a fractionalized phase with topological order.