Measuring Topological Order

Abstract

The topological order of a (2+1)D topological phase of matter is characterized by its chiral central charge and a unitary modular tensor category that describes the universal fusion and braiding properties of its anyonic quasiparticles. I discuss the topologically invariant quantities associated with these and identify ones that are useful for determining the topological order. I propose a variety of physical experiments that probe these quantities and detail the relation of the measured data to the topological invariants.

arXiv comment32 pages, 10 figures; v2: minor corrections and updates

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• Methods for simulating string-net states and anyons on a digital quantum computer
• Entanglement in tripartitions of topological orders: a diagrammatic approach
• Anyonic Topological Order in Twisted Equivariant Differential (TED) K-Theory
• Numerical simulation of non-abelian anyons
• Characterizing the Entanglement of Anyonic Systems using the Anyonic Partial Transpose
• Extending the planar theory of anyons to quantum wire networks
• Phases of Interacting Fibonacci Anyons on a Ladder at Half-Filling