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Keyword: gauging ×Clear all

3 claims from 1 paper

1. Physics and Astronomy › Quantum many-body systems

   Symmetry fractionalization, defects, and gauging of topological phases

   Barkeshli, Bonderson, Cheng and Wang · Physical review. B./Physical review. B · 2019

   The paper develops a general framework for how symmetry interacts with topological order in 2+1 dimensions, covering symmetry fractionalization, symmetry defects and the gauging of symmetries.

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   1. UncheckedThe authors build a theory of symmetry defects (fluxes) that classifies symmetry-enriched topological phases arising from a topological phase C with symmetry group G.“We develop a theory of extrinsic defects (fluxes) associated with elements of the symmetry group, which provides a general classification of symmetry-enriched topological phases derived from a topological phase of matter $\mathcal{C}$ with symmetry group $G$.”
   2. UncheckedThe algebraic theory of symmetry defects, a G-crossed braided tensor category, lets researchers compute many properties of these defects in topological phases.“The algebraic theory of the defects, known as a $G$-crossed braided tensor category $\mathcal{C}_{G}^{\times}$, allows one to compute many properties, such as the number of topologically distinct types of defects associated with each group element, their fusion rules, quantum dimensions, zero modes…”
   3. Unchecked“We also examine the promotion of the global symmetry to a local gauge invariance, wherein the extrinsic $G$-defects are turned into deconfined quasiparticle excitations, which results in a different topological phase $(\mathcal{C}_{G}^{\times})^{G}$.”