Fusion Structure from Exchange Symmetry in (2+1)-Dimensions
arXiv:2004.06282 · doi:10.1016/j.aop.2021.168471
Abstract
Until recently, a careful derivation of the fusion structure of anyons from some underlying physical principles has been lacking. In [Shi et al., Ann. Phys., 418 (2020)], the authors achieved this goal by starting from a conjectured form of entanglement area law for 2D gapped systems. In this work, we instead start with the principle of exchange symmetry, and determine the minimal prescription of additional postulates needed to make contact with unitary ribbon fusion categories as the appropriate algebraic framework for modelling anyons. Assuming that 2D quasiparticles are spatially localised, we build a functor from the coloured braid groupoid to the category of finite-dimensional Hilbert spaces. Using this functor, we construct a precise notion of exchange symmetry, allowing us to recover the core fusion properties of anyons. In particular, given a system of quasiparticles, we show that the action of a certain -braid uniquely specifies its superselection sectors. We then provide an overview of the braiding and fusion structure of anyons in the usual setting of braided fusion systems. By positing the duality axiom of [A. Kitaev, Ann. Phys., 321(1) (2006)] and assuming that there are finitely many distinct topological charges, we arrive at the framework of ribbon categories.
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References in corpus (10)
- Fault-tolerant quantum computation by anyons
- Anyons in an exactly solved model and beyond
- Topological orders and Edge excitations in FQH states
- Quantum Entanglement in Fermionic Lattices
- Topological phases with parafermions: theory and blueprints
- Fermionic Modular Categories and the 16-fold Way
- Weyl spin liquids
- Classification of Rank 5 Premodular Categories
- Fusion rules from entanglement
- Beyond Anyons