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Symmetry fractionalization, defects, and gauging of topological phases
We examine the interplay of symmetry and topological order in $2+1$ dimensional topological phases of matter. We present a definition of the topological symmetry group, which characterizes the
Theory of defects in Abelian topological states
The structure of extrinsic defects in topologically ordered states of matter is host to a rich set of universal physics. Extrinsic defects in 2+1 dimensional topological states include line-like
Twist defects and projective non-Abelian braiding statistics
It has recently been realized that a general class of non-Abelian defects can be created in conventional topological states by introducing extrinsic defects, such as lattice dislocations or
Higgs mechanism in higher-rank symmetric U(1) gauge theories
We use the Higgs mechanism to investigate connections between higher-rank symmetric $U(1)$ gauge theories and gapped fracton phases. We define two classes of rank-2 symmetric $U(1)$ gauge theories:
Modular transformations through sequences of topological charge projections
The ground-state subspace of a topological phase of matter forms a representation of the mapping class group of the space on which the state is defined. We show that elements of the mapping class
Non-Fermi liquids and the Wiedemann-Franz law
A general discussion of the ratio of thermal and electrical conductivities in non-Fermi liquid metals is given. In metals with sharp Drude peaks, the relevant physics is correctly organized around
Topological Nematic States and Non-Abelian Lattice Dislocations
An exciting new prospect in condensed matter physics is the possibility of realizing fractional quantum Hall (FQH) states in simple lattice models without a large external magnetic field. A
Continuous transition between fractional quantum Hall and superfluid states
We develop a theory of a direct, continuous quantum phase transition between a bosonic Laughlin fractional quantum Hall (FQH) state and a superfluid, generalizing the Mott insulator to superfluid
Charge 2e/3 Superconductivity and Topological Degeneracies without Localized Zero Modes in Bilayer Fractional Quantum Hall States.
  • M. Barkeshli
  • Physics, Medicine
    Physical review letters
  • 3 April 2016
It is demonstrated that an analog of non-Abelian braiding is possible, despite the absence of a localized zero mode, and the superconductor induces charge 2e/3 quasiparticle-pair condensation at each boundary of the FQH state.
Translational symmetry and microscopic constraints on symmetry-enriched topological phases: a view from the surface
The Lieb-Schultz-Mattis theorem and its higher dimensional generalizations by Oshikawa and Hastings require that translationally invariant 2D spin systems with a half-integer spin per unit cell must