Phase transitions are among the most complex and intriguing phenomena in physics. The Landau-Ginzburg-Wilson-Fisher theory of phase transitions, associated with the onset of a spontaneously broken symmetry, is one of the foundations of modern statistical mechanics and condensed-matter theory. However, the discovery of topological phases of matter as well as a growing number of surprising experiments in strongly correlated electron systems calls for a new understanding for phase transitions beyond the Landau paradigm. 

In this talk, we will present results on novel quantum critical points in 3 spatial dimensions. In particular, we will demonstrate the breakdown of the Landau-Ginzburg-Wilson-Fisher framework even for a standard quantum phase transition between a symmetric phase and a broken symmetry phase. Synthesizing new development on Yang-Mills gauge theories and their quantum anomalies, we will describe the existence of a critical theory expressed in terms of emergent fermions coupled with deconfined gauge fields instead of fluctuating order parameter. We dub such phase transitions “Landau ordering phase transitions beyond Landau description”. If time permits, we will also discuss deconfined quantum phase transitions between topological phases of matter, and some unprecedented critical phenomena we discover along these explorations.