Disorder operators in (2+1)d quantum phases

Abstract: Defects have been playing an increasingly important role in our understanding of quantum phases of matter and quantum field theories in general. Closed defects can be created by applying the associated symmetry transformation, known as a disorder operator, to a finite region.  Expectation value of the disorder operator in a symmetry-preserving ground state contains universal information about the underlying state. In this talk I will examine physical implications of scaling behavior of disorder parameter and how they lead to new many-body invariants in different classes of (2+1)d quantum phases, including both gapped and gapless systems.