Topological terms in effective theories of two dimensional quantum magnets

Abstract Effective theories are derived for paramagnetic states which arise out of competing orders in quantum antiferromagnets in two spatial dimensions. Our focus is on properly salvaging Berry phase terms, which can, if present, alter ground state properties and induce quantum phase transitions. To this end we explicitly incorporate, in addition to the O(3) orientational fluctuations, the competition with valence-bond-solid order, and find that novel topological terms will naturally arise: a Wess–Zumino–Witten-type term for an isotropic system, and a tunable 2+1d θ -term for an anisotropic system with bond alternation. We discuss their physical implications.