Title: Competing orders and anomalies
Cm-Bio 4-16 Moon
Abstract: Current conservation “laws” associated with continuous symmetries could be spoiled by quantum mechanical fluctuations, so-called anomalies. Striking non-perturbative nature of anomalies deepens our understanding in topological phases in condensed matters as well as in high energy physics. Here, we investigate a different class of anomalies in condensed matters, anomalies in quantum phase transitions between competing orders, described by non-linear sigma models with the WessZumino-Witten term. The models were proposed to describe physics beyond conventional LandauGinzburg-Wilson paradigm, and we show how the models’ universality class is different from LandauGinzburg-Wilson theory’s in two and four spacetime dimensions. The presence of anomalies and their matching condition play a crucial role. In a context of competing orders, we obtain nonperturbative results from anomalies, for example, criteria of deconfined quantum criticality in three spatial dimensions and constraints on gauge structure of spin liquids. Physical realizations of the anomalies such as the two color quantum chromodynamics as well as Weyl semi-metals with all-in all-out order parameter are also discussed.