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.
Highlights
Topological phases of matter may possess emergent quasiparticle excitations that exhibit exotic exchange statistics, such as anyons in (2 + 1)D systems [1,2]
The topological order of a (2 + 1)D topological phase, i.e., the collection of universal properties associated with the phase, is understood to be fully characterized by the combination of (1) the chiral central charge, which is associated with the chiral thermal transport of gapless edge modes, and (2) a unitary modular tensor category (UMTC) [3,4,5], which specifies the fusion and braiding properties of the quasiparticle excitations
There is no single experiment that serves as a conclusive “smoking gun” for determining the topological order of a topological phase
Summary
Topological phases of matter may possess emergent quasiparticle excitations that exhibit exotic exchange statistics, such as anyons in (2 + 1)D systems [1,2]. From the perspective of designing physical experiments, it is important to identify experiments probing these gauge invariants that both collect a complete (or near-complete) characterization of the UMTC, and which do so with methods that allow the invariants to be carefully separated from nonuniversal effects It is crucial for the experiments not to rely upon fine-tuning, precise knowledge of the microscopic Hamiltonian, or other unrealistic assumptions. Properties that are vulnerable to such effects include overall phases of transformations and ground state degeneracy on higher genus surfaces In this regard, it is expected that the properties measured by the bulk quasiparticle experiments of Sec. III will remain topologically protected
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