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arXiv · 1012.2417

Phase transitions in Z_N gauge theory and twisted Z_N topological phases

Maissam Barkeshli·Xiao-Gang Wen
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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 $U(1) \times U(1) \rtimes Z_2$ Chern-Simons (CS) field theory. The $U(1) \times U(1) \rtimes Z_2$ 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.

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Maissam Barkeshli, Xiao-Gang Wen. 2010-12-11. Phase transitions in Z_N gauge theory and twisted Z_N topological phases. https://doi.org/10.1103/physrevb.86.085114

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