Analog of Lieb-Schultz-Mattis argument for low dimensional antiferromagnets in the semiclassical sigma model framework

We revisit the Lieb-Schultz-Mattis argument as generalized by Oshikawa, and discuss how the program can be carried through in the sigma model + topological term effective action framework for antiferromagnets. We emphasize the role played by large gauge transformations, which effect the ground state Schroedinger wave functional in subtle but nevertheless crucial ways. The same language will be employed to see how entanglement properties are governed by the topological terms. We will also discuss how the above relates to the AKLT wavefunction.