Abstract

The ideas of quantum criticality have proven a powerful unifying tool for a broad range of strongly correlated quantum systems. I will review the basic notions underlying quantum criticality and the different types of systems to which they apply.

I will concentrate in particular upon quantum criticality in metals. Although the term quantum criticality was first coined in the study of such systems, there is strong evidence from both experiment and theory that metallic quantum critical points are intrinsically unstable. I will describe a recently developed approach to understanding this instability in terms of quantum order-by-disorder.

I will briefly compare this to other techniques such as the critical nodal surface and the remarkable AdS/CFT correspondence. I will end with some speculations about the relationship between these various approaches and the direction in which a synthesis might eventually be found.