Phase transitions in ZN gauge theory and twisted ZN topological phases

Abstract

We find a series of non-Abelian topological phases that are separated from the deconfined phase of Z[subscript N] gauge theory by a continuous quantum phase transition. These non-Abelian states, which we refer to as the “twisted” Z[subscript N] states, are described by a recently studied U(1)×U(1)⋊Z[subscript 2] Chern-Simons (CS) field theory. The U(1)×U(1)⋊Z[subscript 2] CS theory provides a way of gauging the global Z[subscript 2] electric-magnetic symmetry of the Abelian Z[subscript N] phases, yielding the twisted Z[subscript N] states. We introduce a parton construction to describe the Abelian Z[subscript N] phases in terms of integer quantum Hall states, which then allows us to obtain the non-Abelian states from a theory of Z[subscript 2] fractionalization. The non-Abelian twisted Z[subscript N] states do not have topologically protected gapless edge modes and, for N>2, break time-reversal symmetry.