Phase transitions inZNgauge theory and twistedZNtopological phases

Abstract

We find a series of non-Abelian topological phases that are separated from the deconfined phase of ${Z}_{N}$ gauge theory by a continuous quantum phase transition. These non-Abelian states, which we refer to as the ``twisted'' ${Z}_{N}$ states, are described by a recently studied $U(1)\ifmmode\times\else\texttimes\fi{}U(1)\ensuremath{\rtimes}{Z}_{2}$ Chern-Simons (CS) field theory. The $U(1)\ifmmode\times\else\texttimes\fi{}U(1)\ensuremath{\rtimes}{Z}_{2}$ CS theory provides a way of gauging the global ${Z}_{2}$ electric-magnetic symmetry of the Abelian ${Z}_{N}$ phases, yielding the twisted ${Z}_{N}$ states. We introduce a parton construction to describe the Abelian ${Z}_{N}$ phases in terms of integer quantum Hall states, which then allows us to obtain the non-Abelian states from a theory of ${Z}_{2}$ fractionalization. The non-Abelian twisted ${Z}_{N}$ states do not have topologically protected gapless edge modes and, for $N>2$, break time-reversal symmetry.